(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
The notion of vector bundle in algebraic geometry.
Usually characterized in terms of its sheaf of sections on the locally ringed site (with structure sheaf $\mathcal{O}$) of the given scheme: a locally free $\mathcal{O}$-module of finite rank.
Over the complex numbers, GAGA relates algebraic to holomorphic vector bundles (e.g. Neeman 07, theorem 1.1.4).
Last revised on May 25, 2017 at 11:11:09. See the history of this page for a list of all contributions to it.