Complexifiable characteristic classes

TL;DR

This paper investigates the topological characteristic classes of complexified vector bundles, specifically identifying those originating from the real vector bundles that underlie the complexification process.

Contribution

It precisely determines which characteristic classes of real vector bundles are inherited by their complexified counterparts.

Findings

Characterization of classes from real vector bundles in complexified bundles

Explicit description of topological characteristic classes for complexified bundles

Clarification of the relationship between real and complex vector bundle classes

Abstract

We examine the topological characteristic cohomology classes of complexified vector bundles. In particular, all the classes coming from the real vector bundles underlying the complexification are determined.