(see also Chern-Weil theory, parameterized homotopy theory)
vector bundle, (∞,1)-vector bundle
topological vector bundle, differentiable vector bundle, algebraic vector bundle
direct sum of vector bundles, tensor product of vector bundles, inner product of vector bundles?, dual vector bundle
homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
Introductions
Definitions
Paths and cylinders
Homotopy groups
Basic facts
Theorems
For $X$ a suitable space then a vector bundle over $X$ is called trivial if there is no twist in how the fibers vary over it.
For $X$ a topological space, then a topological vector bundle $E \to X$ over a topological field $k$ is called trivial if its total space is the product topological space
with the topological vector space $k^n$, for some $n \in \mathbb{N}$. For $n = 1$, one also speaks of a trivial line bundle.
An isomorphism of vector bundles over $X$ of the form
is called a trivialization of $E$. If $E$ admits such an isomorphis, then it is called a trivializable vector bundle.
Last revised on July 22, 2017 at 09:53:58. See the history of this page for a list of all contributions to it.