Nonvanishing vector fields on orbifolds

Authors:
Carla Farsi and Christopher Seaton

Journal:
Trans. Amer. Math. Soc. **362** (2010), 509-535

MSC (2000):
Primary 22A22, 57R25; Secondary 55S91, 58H05

DOI:
https://doi.org/10.1090/S0002-9947-09-04938-1

Published electronically:
August 7, 2009

MathSciNet review:
2550162

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Abstract: We introduce a complete obstruction to the existence of nonvanishing vector fields on a closed orbifold . Motivated by the inertia orbifold, the space of multi-sectors, and the generalized orbifold Euler characteristics, we construct for each finitely generated group an orbifold called the space of -sectors of . The obstruction occurs as the Euler-Satake characteristics of the -sectors for an appropriate choice of ; in the case that is oriented, this obstruction is expressed as a cohomology class, the -Euler-Satake class. We also acquire a complete obstruction in the case that is compact with boundary and in the case that is an open suborbifold of a closed orbifold.

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Additional Information

**Carla Farsi**

Affiliation:
Department of Mathematics, University of Colorado at Boulder, Campus Box 395, Boulder, Colorado 80309-0395

Email:
farsi@euclid.colorado.edu

**Christopher Seaton**

Affiliation:
Department of Mathematics and Computer Science, Rhodes College, 2000 N. Parkway, Memphis, Tennessee 38112

Email:
seatonc@rhodes.edu

DOI:
https://doi.org/10.1090/S0002-9947-09-04938-1

Keywords:
Orbifold,
orbifold with boundary,
vector field,
orbifold Euler characteristic,
orbifold Euler class,
orbifold sector

Received by editor(s):
August 12, 2008

Published electronically:
August 7, 2009

Additional Notes:
The second author was partially supported by a Rhodes College Faculty Development Endowment Grant.

Article copyright:
© Copyright 2009
American Mathematical Society