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Bundle in which the fiber is a surface
In mathematics, a surface bundle is a bundle in which the fiber is a surface. When the base space is a circle the total space is three-dimensional and
Surface_bundle
In mathematics, a surface bundle over the circle is a fiber bundle with base space a circle, and with fiber space a surface. Therefore the total space
Surface bundle over the circle
Surface_bundle_over_the_circle
Topological space
a , b ) {\displaystyle (a,b)} with a > 0 {\displaystyle a>0} is the surface bundle of the automorphism of a disk given by rotation by an angle of 2 π b
Seifert_fiber_space
Transport system component in vascular plants
mesophyll cells lie between the bundle sheath and the leaf surface. The Calvin cycle is confined to the chloroplasts of these bundle sheath cells in C4 plants
Vascular_bundle
Concept in algebraic geometry
canonical bundle of a non-singular algebraic variety V {\displaystyle V} of dimension n {\displaystyle n} over a field is the line bundle Ω n = ω {\displaystyle
Canonical_bundle
Collection of heart muscle cells
The bundle of His (BH) or His bundle (HB) (/hɪs/ "hiss") is a collection of heart muscle cells specialized for electrical conduction. As part of the electrical
Bundle_of_His
Type of vector bundle
'Higgs bundle', and the condition φ ∧ φ = 0 {\displaystyle \varphi \wedge \varphi =0} (which is vacuous in Hitchin's original set-up on Riemann surfaces) was
Higgs_bundle
Conjecture pertaining to finite covers of 3-manifold subfields
3-manifold with infinite fundamental group has a finite cover which is a surface bundle over the circle. A 3-manifold which has such a finite cover is said
Virtually_fibered_conjecture
A torus bundle, in the sub-field of geometric topology in mathematics, is a kind of surface bundle over the circle, which in turn is a class of three-manifolds
Torus_bundle
Mathematical parametrization of vector spaces by another space
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X
Vector_bundle
of the Surface devices, the initial release of the Surface and Surface Pro had bundle options, which bundled the black Touch Cover. The Surface Pen has
List of Microsoft Surface accessories
List_of_Microsoft_Surface_accessories
Possibility of a consistent definition of "clockwise" in a mathematical space
also be expressed in terms of the tangent bundle. The tangent bundle is a vector bundle, so it is a fiber bundle with structure group GL ( n , R ) {\displaystyle
Orientability
Type of smooth complex surface of kodaira dimension 0
"K3 surface" In mathematics, a complex analytic K3 surface is a compact connected complex manifold of dimension 2 with а trivial canonical bundle and
K3_surface
Mathematical space
I-bundles Knot and link complements Lens space Seifert fiber spaces, Circle bundles Spherical 3-manifold Surface bundles over the circle Torus bundle A
3-manifold
24 mathematical problems stated in 1982
conjecture: every hyperbolic 3-manifold have a finite cover which is a surface bundle over the circle. Solved by Ian Agol. 2013 19th Describe topology and
Thurston's_24_questions
Fiber bundle whose fibers are projective spaces
O*) only if the projective bundle is the projectivization of a vector bundle. In particular, if X is a compact Riemann surface then H2(X,O*)=0, and so this
Projective_bundle
Manifold of dimension 3 equipped with a hyperbolic metric
hyperbolic metric of finite volume. A particular case is that of a surface bundle over the circle: such manifolds are always irreducible, and they carry
Hyperbolic_3-manifold
Intrinsic geometric structures in mathematics
form with principal bundles only in the 1950s. The classical nineteenth century approach to the differential geometry of surfaces, due in large part to
Riemannian connection on a surface
Riemannian_connection_on_a_surface
Principal fiber bundle
bundle is a fiber bundle where the fiber is the circle S 1 {\displaystyle S^{1}} . Oriented circle bundles are also known as principal U(1)-bundles,
Circle_bundle
Differentiable function whose derivative is everywhere injective
normal bundles plus trivial bundles, and thus if the stable normal bundle has cohomological dimension k, it cannot come from an (unstable) normal bundle of
Immersion_(mathematics)
Quillen determinant line bundle is a line bundle over the space of Cauchy–Riemann operators of a vector bundle over a Riemann surface, introduced by Quillen (1985)
Quillen determinant line bundle
Quillen_determinant_line_bundle
Ruled surface over the projective line
{\mathcal {O}}(1)} , the invertible sheaf or line bundle with associated Cartier divisor a single point. The surface Σ 0 {\displaystyle \Sigma _{0}} is isomorphic
Hirzebruch_surface
Continuous surjection satisfying a local triviality condition
In mathematics, and particularly topology, a fiber bundle (Commonwealth English: fibre bundle) is a space that is locally a product space, but globally
Fiber_bundle
Straight path on a curved surface or a Riemannian manifold
double tangent bundle TTM into horizontal and vertical bundles: T T M = H ⊕ V . {\displaystyle TTM=H\oplus V.} The double tangent bundle can be visualized
Geodesic
of I-bundles when the base manifold is any surface but the Klein bottle K {\displaystyle K} . That surface has three I-bundles: the trivial bundle K ×
I-bundle
Relation between genus, degree, and dimension of function spaces over surfaces
holomorphic line bundles on a Riemann surface, the theorem can also be stated in a different, yet equivalent way: let L be a holomorphic line bundle on X. Let
Riemann–Roch_theorem
Construction of combinatorial group theory
that has been 'glued back' on itself by a mapping f : X → X (see e.g. Surface bundle over the circle). Thus, HNN extensions describe the fundamental group
HNN_extension
sets of sections of the Horrocks–Mumford bundle are abelian surfaces of degree 10, called Horrocks–Mumford surfaces. By computing Chern classes one sees that
Horrocks–Mumford_bundle
Correspondsnce between Higgs bundles and fundamental group representations
correspondence between stable vector bundles and unitary representations of the fundamental group of a compact Riemann surface. In fact the Narasimhan–Seshadri
Nonabelian Hodge correspondence
Nonabelian_Hodge_correspondence
Study of vector bundles, principal bundles, and fibre bundles
theory is the general study of connections on vector bundles, principal bundles, and fibre bundles. Gauge theory in mathematics should not be confused
Gauge_theory_(mathematics)
One-dimensional complex manifold
positive line bundle on any complex curve. The existence of non-constant meromorphic functions can be used to show that any compact Riemann surface is a projective
Riemann_surface
Concept in algebraic geometry
geometry, a line bundle on a projective variety is nef if it has nonnegative degree on every curve in the variety. The classes of nef line bundles are described
Nef_line_bundle
Vector bundles theorem
(projectively) flat connection over the Riemann surface. The notion of a Hermitian–Einstein connection for a vector bundle over a higher dimensional complex manifold
Kobayashi–Hitchin correspondence
Kobayashi–Hitchin_correspondence
Fiber bundle Principal bundle Frame bundle Hopf bundle Associated bundle Vector bundle Tangent bundle Cotangent bundle Line bundle Jet bundle Sheaf (mathematics)
List of differential geometry topics
List_of_differential_geometry_topics
Concept in algebraic geometry
an ample line bundle, although there are several related classes of line bundles. Roughly speaking, positivity properties of a line bundle are related to
Ample_line_bundle
Anatomical cardiac structure
In the heart's conduction system, Bachmann's bundle (also called the Bachmann bundle or the interatrial band) is a branch of the anterior internodal tract
Bachmann's_bundle
Group of isotopy classes of a topological automorphism group
in Thurston's theory of geometric three-manifolds (for example, to surface bundles). The elements of this group have also been studied by themselves:
Mapping_class_group
In Euclidean geometry, the bundle theorem is a statement about six circles and eight points in the Euclidean plane. In general incidence geometry, it is
Bundle_theorem
Mathematic theorem about Riemann surfaces
Narasimhan and Seshadri (1965), says that a holomorphic vector bundle over a compact Riemann surface is stable if and only if it comes from an irreducible projective
Narasimhan–Seshadri_theorem
Mathematics theory
to the existence of a canonical indigenous bundle over the Riemann surface: the unique indigenous bundle that is invariant under complex conjugation
P-adic_Teichmüller_theory
Type of fiber bundle on a Riemann surface
indigenous bundle on a Riemann surface is a fiber bundle with a flat connection associated to some complex projective structure. Indigenous bundles were introduced
Indigenous_bundle
Construct allowing differentiation of tangent vector fields of manifolds
simplest methods of defining differentiation of the sections of vector bundles. The notion of an affine connection has its roots in 19th-century geometry
Affine_connection
Mathematical classification of surfaces
Hirzebruch surfaces Σn for n = 0 or n ≥ 2. (The Hirzebruch surface Σn is the P1 bundle over P1 associated to the sheaf O(0) + O(n). The surface Σ0 is isomorphic
Enriques–Kodaira classification
Enriques–Kodaira_classification
Organ found in humans and other animals
atrioventricular node only. The signal then travels along the bundle of His to left and right bundle branches through to the ventricles of the heart. In the
Heart
Muscle band in the right ventricle of the heart
moderator band consists of conductive tissue branching off of the right bundle branch (within the ventricular septum) and wrapped in working cardiac muscle
Moderator_band
divided into two subtypes: primary Kodaira surfaces with trivial canonical bundle, and secondary Kodaira surfaces which are quotients of these by finite groups
Kodaira_surface
Aspect of heart function
the right atrium to the atrioventricular node, along the bundle of His, and through the bundle branches to Purkinje fibers in the walls of the ventricles
Cardiac_conduction_system
On the Euler characteristic of a holomorphic vector bundle on a compact complex manifold
class of the tangent bundle of X. Significant special cases are when E is a complex line bundle, and when X is an algebraic surface (Noether's formula)
Hirzebruch–Riemann–Roch theorem
Hirzebruch–Riemann–Roch_theorem
Arteries transporting blood to heart muscle
Myocardium Conduction system cardiac pacemaker SA node Bachmann's bundle AV node bundle of His bundle branches Purkinje fibers Pericardial cavity Pericardial sinus
Coronary_arteries
Tablet computer from Microsoft
Surface Go 4 Bundle". www.microsoft.com. Retrieved 2025-06-21. "Microsoft Surface Go 4 Features". www.microsoft.com. Retrieved 2025-06-21. "Surface Go
Surface_Go_4
Electric conductors in heart ventricles
The bundle branches, or Tawara branches, transmit cardiac action potentials (electrical signals) from the bundle of His to Purkinje fibers in heart ventricles
Bundle_branches
Concept in algebraic geometry
Kunihiko Kodaira. The canonical bundle of a smooth algebraic variety X of dimension n over a field is the line bundle of n-forms, K X = ⋀ n Ω X 1 , {\displaystyle
Kodaira_dimension
Partial differential equations whose solutions are instantons
of partial differential equations for a connection on a vector bundle or principal bundle. They arise in physics as the Euler–Lagrange equations of the
Yang–Mills_equations
System of partial differential equations used in Higgs field theory
equations for a connection and Higgs field on a vector bundle or principal bundle over a Riemann surface, written down by Nigel Hitchin in 1987. Hitchin's
Hitchin's_equations
Mathematical concept
how elliptic surfaces fit into the classification of surfaces, it is important to compute the canonical bundle of a minimal elliptic surface f: X → S. Over
Elliptic_surface
decomposition Branched surface Lamination Examples 3-sphere Torus bundles Surface bundles over the circle Graph manifolds Knot complements Whitehead manifold
List of geometric topology topics
List_of_geometric_topology_topics
gives conditions for a line bundle on a projective surface to be very ample. Let D be a nef divisor on a smooth projective surface X. Denote by KX the canonical
Reider's_theorem
Muscular tissue of heart in vertebrates
relatively slow rate between the cells. Specialized conductive cells in the bundle of His, and the Purkinje fibers are larger in diameter and conduct signals
Cardiac_muscle
principal bundles was introduced by Annamalai Ramanathan for the purpose of defining the moduli space of G-principal bundles over a Riemann surface, a generalisation
Stable_principal_bundle
Mathematics of smooth surfaces
manifold, to differential operators on the tangent bundle or frame bundle. In the case of an embedded surface, the lift to an operator on vector fields, called
Differential geometry of surfaces
Differential_geometry_of_surfaces
Sensory hair in the inner ear
the hair bundle, the kinocilium is found in the center of the apical surface of the hair cell surrounded by 20-300 microvilli. During hair bundle morphogenesis
Kinocilium
Valve in the human heart between the left ventricle and the aorta
model of Cardiac Biological Valve Prosthesis. Front of thorax, showing surface relations of bones, lungs (purple), pleura (blue), and heart (red outline)
Aortic_valve
Circulation of blood in the blood vessels of the heart muscle (myocardium)
not give rise to a vessel. Coronary vessel branches that remain on the surface of the heart and follow the sulci of the heart are called epicardial coronary
Coronary_circulation
Branch of mathematics
differential geometry. A smooth manifold always carries a natural vector bundle, the tangent bundle. Loosely speaking, this structure by itself is sufficient only
Differential_geometry
Differential geometry topic
tangent k-planes in the tangent bundle TM. The target space for the Gauss map N is a Grassmann bundle built on the tangent bundle TM. In the case where M =
Gauss_map
Private network of connections between trusted peers
be accessed via a customized browser from Vidalia (aka the Tor browser bundle), or alternatively via a proxy configured to perform the same function.
Darknet
Reproductive structure in flowering plants
produced by structural coloration, in which colour is produced by tiny surface structures interfering with waves of light. This includes iridescence (as
Flower
Metric on a determinant line bundle
determinant line bundle of a family of operators. It was introduced by Daniel Quillen for certain elliptic operators over a Riemann surface, and generalized
Quillen_metric
X^{2}+aXY+bY^{2}=P(T).\,} Conic bundles can be considered as either a Severi–Brauer or Châtelet surface. This can be a double covering of a ruled surface. It can be associated
Conic_bundle
Class of annelid worms
movement and, in many species, act as the worm's primary respiratory surfaces. Bundles of bristles, the chaetae, project from the parapodia. However, polychaete
Polychaete
Type of heat exchanger that uses ambient air as the cooling medium
applicable to ACHEs; reduction of effective surface area can only be achieved by valving off complete tube bundles. Where the process fluid is susceptible
Air_cooled_heat_exchanger
High frequency optimised electric wire
several levels of bundling (already-twisted wires are twisted together into small bundles, which are then twisted into larger bundles, etc.). The result
Litz_wire
Double-walled sac containing the heart and roots of the great vessels
the bottom (where only the serous pericardium exists to cover the upper surface of the central tendon of diaphragm). The fibrous pericardium is semi-rigid
Pericardium
Fibre secreted by some molluscs
(/ˈbɪsəs/) is a bundle of filaments secreted by many species of bivalve mollusc that function to attach the mollusc to a solid surface. Species from several
Byssus
Riemannian manifold with SU(n) holonomy
bundle. If a compact Kähler manifold is simply connected, then the weak definition above is equivalent to the stronger definition. Enriques surfaces give
Calabi–Yau_manifold
Algebraic variety of dimension two
cubic surfaces, Veronese surface, del Pezzo surfaces, ruled surfaces κ = 0 : K3 surfaces, abelian surfaces, Enriques surfaces, hyperelliptic surfaces κ =
Algebraic_surface
Mathematics concept
neighborhood of an orientable surface in an orientable 3-manifold is just a "thickened up" version of the surface, i.e., a trivial I-bundle. So the regular neighborhood
Haken_manifold
vector bundle is a (holomorphic or algebraic) vector bundle that is stable in the sense of geometric invariant theory. Any holomorphic vector bundle may
Stable_vector_bundle
Mathematical theorem
the trivial bundle, and is equal to 1 + p a {\displaystyle 1+p_{a}} , where p a {\displaystyle p_{a}} is the arithmetic genus of the surface. For comparison
Riemann–Roch theorem for surfaces
Riemann–Roch_theorem_for_surfaces
Chamber of the heart
adult. Its upper front surface is circled and convex, and forms much of the sternocostal surface of the heart. Its under surface is flattened, forming
Ventricle_(heart)
Topological space that locally resembles Euclidean space
and there is no intrinsic notion of a normal bundle, but instead there is an intrinsic stable normal bundle. The n-sphere Sn is a generalisation of the
Manifold
Cleaning tool made up of coarse strings
A mop (such as a floor mop) is a mass or bundle of coarse strings or yarn, etc., or a piece of cloth, sponge or other absorbent material, attached to a
Mop
Part of the human heart
right auricle, lat: auricula atrii dextra) is located at the front upper surface of the right atrium. Looking from the front, the right atrial appendage
Atrium_(heart)
Chern number of a rank 2 vector bundle on a surface is the number of zeroes of a generic section. For a Fano surface S, a 1-form w defines also a hyperplane
Fano_surface
Structure binding nerves and vessels
A neurovascular bundle is a structure that binds nerves and veins (and in some cases arteries and lymphatics) with connective tissue so that they travel
Neurovascular_bundle
Concept in algebraic geometry
surfaces of degree at least 3. A del Pezzo surface is a complete non-singular surface with ample anticanonical bundle. There are some variations of this definition
Del_Pezzo_surface
) {\displaystyle \operatorname {Pic} ^{0}(A)} is called a degree 0 line bundle on A. To A one then associates a dual abelian variety Av (over the same
Dual_abelian_variety
In algebraic geometry, the Iitaka dimension of a line bundle L on an algebraic variety X is the dimension of the image of the rational map to projective
Iitaka_dimension
be found at the n-Category Café: Bundle Gerbes: General Idea and Definition Bundle Gerbes: Connections and Surface Transport Gerbe Orbifold Gajer, Pawel
Bundle_gerbe
In mathematics, vector bundles on algebraic curves may be studied as holomorphic vector bundles on compact Riemann surfaces, which is the classical approach
Vector bundles on algebraic curves
Vector_bundles_on_algebraic_curves
Group of cells in the wall of the heart
system (SA node labeled 1) Schematic representation of the atrioventricular bundle Cardiac pacemaker Cardiology Heart block Sinus bradycardia Sinus tachycardia
Sinoatrial_node
In mathematics, a Castelnuovo surface is a surface of general type such that the canonical bundle is very ample and such that c12 = 3pg − 7. Guido Castelnuovo
Castelnuovo_surface
Surface containing a line through every point
projective bundle of a 2-dimensional vector bundle over some curve. The ruled surfaces with base curve of genus 0 are the Hirzebruch surfaces. Doubly ruled
Ruled_surface
Superconductivity theory
just equals the degree of the line bundle; as a result, one may write a line bundle on a Riemann surface as a flat bundle, with N singular points and a covariantly
Ginzburg–Landau_theory
Valve in the heart connecting the left atrium and left ventricle
tissue that thickens the spongiosa layer of the cusp and separates collagen bundles in the fibrosa. This weakens the cusps and adjacent tissue, resulting in
Mitral_valve
Muscular columns found in the heart
are rounded or irregular muscular columns which project from the inner surface of the right and left ventricle of the heart. These are different from
Trabeculae_carneae
Genus of vines
tests of fiber bundles isolated from the inner surface provide insight this basic strut element of the luffa sponges. These fiber bundles vary in diameter
Luffa
Characterizes homeomorphisms of a compact orientable surface
pseudo-Anosov. The case where S is a torus (i.e., a surface whose genus is one) is handled separately (see torus bundle) and was known before Thurston's work. If
Nielsen–Thurston classification
Nielsen–Thurston_classification
Digital pen made by Microsoft
strokes when it comes into contact with the display. It was bundled with the Surface Pro and Surface Pro 2, but is not compatible with other models. The button
Surface_Pen
Diffeomorphism that has a hyperbolic structure on the tangent bundle
tangent bundle of unit-length vectors on H. Note that a bundle of unit-length vectors on a surface is the principal bundle of a complex line bundle. One
Anosov_diffeomorphism
SURFACE BUNDLE
SURFACE BUNDLE
Boy/Male
Irish Gaelic
Surname.
Boy/Male
Indian
Part of Sun
Boy/Male
Irish
Surname.
Boy/Male
Irish
Surname.
Boy/Male
Irish
Surname.
Boy/Male
Scottish American English
Surname.
Boy/Male
Irish Gaelic
Surname.
Boy/Male
Irish American Welsh Scandinavian Scottish English
Surname.
Surname or Lastname
Probably an Americanized spelling of the Swiss German surname Bunz (see Bunce).English
Probably an Americanized spelling of the Swiss German surname Bunz (see Bunce).English : possibly a variant of Bunt.
Boy/Male
Indian, Sanskrit
Surface of the Earth
Boy/Male
Irish
Surname.
Boy/Male
Irish American Welsh
Surname.
Boy/Male
Irish
Surname.
Surname or Lastname
English (Cumbria and Durham)
English (Cumbria and Durham) : variant spelling of Furness.
Boy/Male
Irish
Surname.
Boy/Male
Irish American Biblical Hebrew
Surname.
Boy/Male
Irish American English
Surname.
Boy/Male
Irish
Surname.
Boy/Male
Irish
Surname.
Boy/Male
Irish
Surname.
SURFACE BUNDLE
SURFACE BUNDLE
Girl/Female
Indian
Gift
Girl/Female
Afghan, Arabic, Muslim
Helper; Supporter
Girl/Female
Hindu, Indian, Tamil
Protected; To Guard
Boy/Male
Hindu
Boy/Male
Christian & English(British/American/Australian)
Of God-Like Power
Male
Italian
Italian, Portuguese and Spanish form of Latin Virgilius, possibly VIRGILIO means "flourishing."Â
Boy/Male
Hindu
Wish to have peace
Female
English
(שָׂרָה) Hebrew name SARAH means "noble lady, princess." In the bible, this is the name that God gave to Sarai, wife of Abraham.
Boy/Male
Muslim/Islamic
Trustworthy reliable
Girl/Female
Indian
Name of prophet muhammads (Pbuh) daughter
SURFACE BUNDLE
SURFACE BUNDLE
SURFACE BUNDLE
SURFACE BUNDLE
SURFACE BUNDLE
n.
Alt. of Serfdom
n.
That part of the side which is terminated by the flank prolonged, and the angle of the nearest bastion.
imp. & p. p.
of Surface
n.
An inclosed place in which heat is produced by the combustion of fuel, as for reducing ores or melting metals, for warming a house, for baking pottery, etc.; as, an iron furnace; a hot-air furnace; a glass furnace; a boiler furnace, etc.
n.
Surface; body; substance.
p. pr. & vb. n.
of Surface
n.
To throw out, or exhale, as from a furnace; also, to put into a furnace.
a.
Having the surface smooth and polished; -- said of leaves, the surfaces of shells, etc.
n.
A form of machine for dressing the surface of wood, metal, stone, etc.
n.
The exterior part of anything that has length and breadth; one of the limits that bound a solid, esp. the upper face; superficies; the outside; as, the surface of the earth; the surface of a diamond; the surface of the body.
n.
A magnitude that has length and breadth without thickness; superficies; as, a plane surface; a spherical surface.
v. t.
To name or call by an appellation added to the original name; to give a surname to.
n.
An instrument for gauging or testing a plane surface. See Surface gauge, under Surface.
n.
Hence, outward or external appearance.
v. t.
To work over the surface or soil of, as ground, in hunting for gold.
v. t.
To give a surface to; especially, to cause to have a smooth or plain surface; to make smooth or plain.
n.
Surface; superficies; externality.
a.
meeting a curve or surface at a point and having at that point the same direction as the curve or surface; -- said of a straight line, curve, or surface; as, a line tangent to a curve; a curve tangent to a surface; tangent surfaces.