vector bundle, 2-vector bundle, (∞,1)-vector bundle
real, complex/holomorphic, quaternionic
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 isomorphism, then it is called a trivializable vector bundle.
Last revised on February 26, 2020 at 19:00:06. See the history of this page for a list of all contributions to it.