Flat vector bundles and open coverings

Abstract

We establish a generic counting formula for the Euler number of a flat vector bundle of rank $2n$ over a $2n$ dimensional closed manifold, in terms of vertices of transversal open coverings of the underlying manifold. We use the Mathai-Quillen formalism to prove our result.

14 pages. Title changed. An error in the previous version was found. The current result counts the Euler number of a flat vector bundle in terms of vertices of transversal open coverings. The Chern conjecture remains open

References in corpus (1)

• Locally homogeneous geometric manifolds

Cited by in corpus (1)

• Affine geometry and Frobenius algebra