Flat vector bundles and open coverings

Huitao Feng; Weiping Zhang

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arXiv · 1603.07248

Flat vector bundles and open coverings

Huitao Feng·Weiping Zhang

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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.

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BibTeX RIS

Huitao Feng, Weiping Zhang. 2016-03-23. Flat vector bundles and open coverings. https://arxiv.org/abs/1603.07248

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