Vector bundle (7770 bytes)
1: ... the curve at that point; this yields the "normal bundle" of the curve.
3: ... be seen as extra structure on an underlying real bundle.
7: A real vector bundle is given by the following data:
10: ...eal number|real]] [[vector space]] on the [[Fiber bundle|fiber]] π^−1({''x''})
12: * πφ(''x'',''v'') = ''x'' for all vectors ''v'' in '''R'''^''n''

Ample vector bundle (2026 bytes)
1: ... of [[complex manifold]]s, a '''very ample [[line bundle]]''' <math>L</math> is one with enough [[section]...
19: An '''ample line bundle''' <math>L</math> is one which becomes very ample...
21: There is a more general theory of ample [[vector bundle]]s.
23: [[Category:Fiber bundles]]

Null vector (vector space) (207 bytes)
1: ... written 0, that is the [[neutral element]] for [[vector addition]].

Associated bundle (5531 bytes)
1: ...ciated bundle''', in which the typical fiber of a bundle changes from <math>F_1</math> to <math>F_2</math>...
5: ...function, with values in ''G''. The '''associated bundle''' construction is just the observation that this...
9: ...F_1</math> to <math>F_2</math>, via the principal bundle. Details in terms of data for an open covering ar...
13: ...sociated <math>G</math>-bundle: this is trite for bundles, but looking at their sections it is essentially...
15: ==Complexifying a real vector bundle==

Bundle (172 bytes)
1: ..., a '''bundle''' is a generalization of a [[fiber bundle]] dropping the condition of a local product struc...
5: [[Category:Fiber bundles]]

Bundle of His (641 bytes)
1: The '''[[bundle of His]]''' is a bundle of heart tissues that transmits the electrical im...
7: Dysfunction of the bundle of His leads to [[heart block]], usually leading ...

Hopf bundle (3380 bytes)
1: ...'''Hopf [[fibration]]''') is a particular [[fiber bundle]] with base space [[sphere|''S''²]], t...
3: ...undle can actually be considered as a [[principal bundle]] when the fiber is identified with the [[circle ...
5: ...viality holds, so that the Hopf bundle is a fiber bundle.
7: :[''a picture of the Hopf bundle would be nice here'']
9: ...diffeomorphic to the 2-sphere. The fibers in this bundle are just the left cosets of U(1) in SU(2).

Jet bundle (3164 bytes)
1: ... on [[Fiber_bundle#Sections|section]]s of a fiber bundle in an invariant form.
3: ...itions on newly-introduced formal variables. Jet bundles are sometimes called '''sprays'''.
7: ... trivial bundle over ''B''. Then sections of this bundle are smooth maps <math>B\to \mathbb R^k</math>. Tw...
11: ...uch maps at ''y'' form the fiber of the first jet bundle at ''y''.
13: The ''n''-th jet bundle is constructed by repeating this operation ''n'' ...

Canonical bundle (1189 bytes)
1: ...</math> of dimension <math>n</math> is the [[line bundle]]
6: ...mega</math> on <math>V</math>. That is, it is the bundle of holomorphic <math>n</math>-forms on <math>V</m...
8: ...icanonical bundle''' is the corresponding inverse bundle <math>\,\!\omega^{-1}</math>.
10: [[Category:Fiber bundles]]

Cotangent bundle (1982 bytes)
1: ...ngent bundle''' of a [[manifold]] is the [[vector bundle]] of all the [[cotangent space]]s at every point ...
5: ...ooth]] [[Fiber bundle|sections]] of the cotangent bundle are differential [[one-form]]s.
7: == The cotangent bundle as phase space ==
11: ...mplectic is a local property: since the cotangent bundle is locally trivial, this definition need only be ...
15: ...ons in a [[dynamical system]], then the cotangent bundle <math>\!\,T^{*}\!M</math> can be thought of as th...

Fiber bundle (8008 bytes)
1: ...possess a different global structure. Every fiber bundle consists of a [[continuous]] [[surjective]] [[map...
3: Fiber bundles play an important role in the fields of [[differ...
7: ...elow. ''B'' is called the '''base space''' of the bundle, ''E'' the '''total space''', and ''F'' the '''fi...
12: [[Image:FiberBundle-01.png|Local triviality condition]]
15: ...>)} is called a '''local trivialization''' of the bundle.

Torus bundle (1882 bytes)
1: ...sub-field of [[geometric topology]], the '''torus bundle''' is a kind of [[3-manifold]].
3: To obtain a '''torus bundle''': let <math>f</math> be an
10: Then <math>M(f)</math> is the torus bundle with [[monodromy]] <math>f</math>.
14: every point of the torus) then the torus bundle <math>M(f)</math> is the
17: Seeing the possible kinds of torus bundles in more detail

Line bundle (4703 bytes)
1: ...fined as a [[vector bundle]] of one-dimensional [[vector space]]s.
3: ...d one-dimensional [[complex number|complex]] line bundles. In fact the topology of the 1&times;1 [[inverti...
5: ...nt bundle (top [[exterior power]]) of the tangent bundle. The [[Möbius band]] corresponds to a double cove...
7: ...ne bundle, we are looking in fact also for circle bundles. There are some celebrated ones, for example the...
9: ==Determinant bundles==

Tangent bundle (1254 bytes)
1: ...tangent bundle''' of a [[manifold]] is a [[vector bundle]] which as a set is the [[disjoint union]] of all...
3: The tangent bundle of manifold ''M'' is usually denoted by ''T''(''M...
7: ''See also'': [[Cotangent bundle]]
10: ...wolfram.com/TangentBundle.html MathWorld: Tangent Bundle]
11: ...cyclopedia/TangentBundle.html PlanetMath: Tangent Bundle]

Bundle of Rights (1803 bytes)
1: The '''bundle of rights''' theory is a common way of explaining...
3: The bundle of rights theory is commonly used in first-year l...
5: ...imately, no owner ever holds the fullest possible bundle. Even the federal government's ownership of land...

Principal bundle (5310 bytes)
1: ...G'' also serves as the [[structure group]] of the bundle.
3: ...ue principal ''G''-bundle from which the original bundle can be reconstructed.
7: ...ibly [[paracompact]]). The abstract fiber of the bundle is taken to be ''G'' itself.
11: The local trivializations of a principal ''G''-bundle are required to be ''G''-[[equivariant]] maps so ...
16: One can also define principal ''G''-bundles in the [[category (mathematics)|category]] of [[...

Medicine bundle (933 bytes)
1: A '''medicine bundle''' is a wrapped [[package]] used by [[Native Amer...
3: ...all size that posesses [[spiritual]] value to the bundle's owner.
5: A medicine bundle can be passed down generationally as an [[inherit...
7: ...[[Shamanistic]] religions. The size of a medicine bundle usually varies from 2 to 14 inches in length.
9: ...]] by the owner. Also, the contents of a medicine bundle are not meant to touch the [[ground]]. This is wh...

Algebra bundle (240 bytes)
1: ...thematics]], an '''algebra bundle''' is a [[fiber bundle]] whose [[fiber]]s are [[algebra over a field|alg...
3: See also: [[vector bundle]].

Spinor bundle (971 bytes)
1: ...SO(p,q)-bundle]] over ''M'' such that its [[fiber bundle|fiber]] is a [[spinor]] [[representations of Lie ...
7: ...e)|connection]] from a connection on the [[vector bundle]] ''V'' (see [[tetrad]]).
13: ...p, so other [[fiber bundle|bundles]] ([[anyon]]ic bundles).
15: See also [[associated bundle]].
22: [[Category:Fiber bundles]]

Bundle theory (7003 bytes)
2: ... view that an [[object (philosophy)|object]] is a bundle, or collection, of [[property|properties]]. Henc...
4: ...ny of its properties. Is that ''possible?'' The bundle theorist says it is not possible. So the apple i...
6: ==Arguments for the bundle theory==
8: The most common sort of argument for the bundle theory capitalizes on the above insights. The ba...
10: This implies, the bundle theorist maintains, that we cannot have any conce...

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