vector bundle, 2-vector bundle, (∞,1)-vector bundle
real, complex/holomorphic, quaternionic
A flat vector bundle is a vector bundle with connection on a vector bundle which is flat. Specifically a flat line bundle is a line bundle with flat connection.
Under the identification of local systems – in the sense of locally constant and locally free abelian sheaves – with flat vector bundles, the flat connection induced on these vector bundles is called the Gauss-Manin connection (e.g. Voisin 2002, Def. 9.13).
Textbook accounts:
Last revised on December 22, 2021 at 21:36:16. See the history of this page for a list of all contributions to it.