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).

References

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

Revised on March 29, 2014 04:50:12 by Urs Schreiber (185.37.147.12)