Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonvanishing vector fields on orbifolds   We introduce a complete obstruction to the existence of nonvanishing vector
fields on a closed orbifold $Q$. Motivated by the inertia orbifold, the space
of multi-sectors, and the generalized orbifold Euler characteristics, we
construct for each finitely generated group $\Gamma$ an orbifold called the
space of $\Gamma$-sectors of $Q$. The obstruction occurs as the Euler-Satake
characteristics of the $\Gamma$-sectors for an appropriate choice of $\Gamma$;
in the case that $Q$ is oriented, this obstruction is expressed as a cohomology
class, the $\Gamma$-Euler-Satake class. We also acquire a complete obstruction
in the case that $Q$ is compact with boundary and in the case that $Q$ is an
open suborbifold of a closed orbifold.

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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an