Flat vector bundles and open coverings
Differential Geometry
2017-09-21 v3 Algebraic Topology
Abstract
We establish a generic counting formula for the Euler number of a flat vector bundle of rank over a 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.
Cite
@article{arxiv.1603.07248,
title = {Flat vector bundles and open coverings},
author = {Huitao Feng and Weiping Zhang},
journal= {arXiv preprint arXiv:1603.07248},
year = {2017}
}
Comments
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