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June 2012 Generalised spin structures on 2-dimensional orbifolds
Hansjörg Geiges, Jesús Gonzalo Pérez
Osaka J. Math. 49(2): 449-470 (June 2012).

Abstract

Generalised spin structures, or $r$-spin structures, on a $2$-dimensional orbifold $\Sigma$ are $r$-fold fibrewise connected coverings (also called $r$\textsuperscript{th} roots) of its unit tangent bundle $ST\Sigma$. We investigate such structures on hyperbolic orbifolds. The conditions on $r$ for such structures to exist are given. The action of the diffeomorphism group of $\Sigma$ on the set of $r$-spin structures is described, and we determine the number of orbits under this action and their size. These results are then applied to describe the moduli space of taut contact circles on left-quotients of the $3$-dimensional geometry $\widetilde{\mathrm{SL}}_{2}$.

Citation

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Hansjörg Geiges. Jesús Gonzalo Pérez. "Generalised spin structures on 2-dimensional orbifolds." Osaka J. Math. 49 (2) 449 - 470, June 2012.

Information

Published: June 2012
First available in Project Euclid: 20 June 2012

zbMATH: 1260.57044
MathSciNet: MR2945757

Subjects:
Primary: 53C27, 53D35, 57M50, 57R18

Rights: Copyright © 2012 Osaka University and Osaka City University, Departments of Mathematics

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Vol.49 • No. 2 • June 2012
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