nLab
flat vector bundle

Contents

Context

Bundles

Differential cohomology

Contents

Idea

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).

References

Textbook accounts:

Last revised on July 25, 2021 at 08:35:38. See the history of this page for a list of all contributions to it.