nLab
complex vector bundle

Contents

Definition

A complex vector bundle is a vector bundle with respect complex vector spaces.

A omplex vector bundle with complex 1-dimensional fibers is a complex line bundle.

Properties

Oka-Grauert principle

The Oka-Grauert principle states that for any Stein manifold XX the holomorphic and the topological classification of complex vector bundles on XX coincide. The original reference is (Grauert 58).

Relation to holomorphic vector bundles

References

  • Emery Thomas, Complex structures on real vector bundles (JSTOR)

In the context of GAGA:

Revised on May 21, 2014 22:16:45 by Urs Schreiber (82.136.246.44)