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arXiv · 0807.2738

Nonvanishing vector fields on orbifolds

Carla Farsi·Christopher Seaton
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Abstract

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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Carla Farsi, Christopher Seaton. 2008-07-17. Nonvanishing vector fields on orbifolds. https://doi.org/10.1090/s0002-9947-09-04938-1

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