Vector bundles

topological construction that makes precise the idea of a family of vector spaces parameterized by another space

tangent spaces of a manifold considered together

vector bundle of all cotangent spaces at every point in a manifold

vector bundle, complementary to the tangent bundle, associated to an embedding

one-dimensional vector bundle

principal bundle associated to a vector bundle, whose fiber is the (torsor over the) automorphism group of the vector-bundle fiber

degree r characteristic class defined for a real oriented vector bundle of rank r on a paracompact space

finite-type sheaf F of modules over a ringed space such that the kernel of a surjective morphism from a finite direct sum of the structure sheaf onto it is also of finite type

linear connection on a vector bundle

classifies holomorphic vector bundles over the complex projective line

the top exterior power of the cotangent bundle of a nonsingular algebraic variety

complex vector bundle on a complex manifold with biholomorphic transition maps

a differentiable manifold whose (co)tangent bundle is topologically trivial

infinitesimal version of a Lie groupoid: manifold M with vector bundle E, vector bundle map ρ: E→TM, and a Lie bracket on sections of E, so that [s,ft] = (ρ(s)f)t+f[s,t] for any function f: M→ℝ and sections s, t of E

vector bundle whose fibers carry the structure of a Clifford algebra

vector bundle whose fibres carry complex structure