(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
Given a vector bundle, its dual is the vector bundle obtained by passing fiber-wise to the dual vector space.
Let $X$ be a topological space and let $E_i \overset{p_i}{\to} X$ be a two topological vector bundles over $X$, of finite rank of a vector bundle. Then a homomorphism of vector bundles
is equivalently a section of the tensor product of vector bundles of $E_2$ with the dual vector bundle of $E_1$.
Moreover, this section is a trivializing section (this example) precisely if the corresponding morphism is an isomorphism.
Last revised on July 4, 2017 at 11:45:37. See the history of this page for a list of all contributions to it.