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 covers of the underlying manifold. We use the Mathai–Quillen formalism to prove our result.
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Feng, H., Zhang, W. (2021). Flat Vector Bundles and Open Covers. In: Manuilov, V.M., Mishchenko, A.S., Nazaikinskii, V.E., Schulze, BW., Zhang, W. (eds) Differential Equations on Manifolds and Mathematical Physics. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-37326-9_9
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DOI: https://doi.org/10.1007/978-3-030-37326-9_9
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-37325-2
Online ISBN: 978-3-030-37326-9
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