(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
A differentiable vector bundle is a vector bundle in the context of differential geometry: a differentiably varying collection of vector space over a given differentiable manifold.
All this for some specified degree of differentiability. If one demands arbitrary differentiabiliy then one speaks of smooth vector bundles over smooth manifolds.
For $X$ a differentiable manifold, then its tangent bundle $T X \to X$ is a differentiable vector bundle, see this lemma.
Last revised on August 1, 2018 at 08:07:14. See the history of this page for a list of all contributions to it.