Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Flat vector bundles and open coverings   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.

31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat