Nonvanishing vector fields on orbifolds
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- by Carla Farsi and Christopher Seaton PDF
- Trans. Amer. Math. Soc. 362 (2010), 509-535 Request permission
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.References
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Additional Information
- Carla Farsi
- Affiliation: Department of Mathematics, University of Colorado at Boulder, Campus Box 395, Boulder, Colorado 80309-0395
- MR Author ID: 311031
- Email: farsi@euclid.colorado.edu
- Christopher Seaton
- Affiliation: Department of Mathematics and Computer Science, Rhodes College, 2000 N. Parkway, Memphis, Tennessee 38112
- MR Author ID: 788748
- Email: seatonc@rhodes.edu
- 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.
- © Copyright 2009 American Mathematical Society
- 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
- MathSciNet review: 2550162