Sheaf of sections of a vector bundle

From Diffgeom
Jump to: navigation, search

Definition

Let M be a differential manifold, and \pi:E \to M be a smooth vector bundle over M. The sheaf of sections of E is defined as follows:

  • To every open subset U of M, it associates the vector space of all smooth sections of the bundle \pi^{-1}(U) \to U
  • The restriction map is section restriction

Facts