Osaka Journal of Mathematics

Generalised spin structures on 2-dimensional orbifolds

Hansjörg Geiges and Jesús Gonzalo Pérez

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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 $\widetilde{\mathrm{SL}}_{2}$.

Article information

Source
Osaka J. Math., Volume 49, Number 2 (2012), 449-470.

Dates
First available in Project Euclid: 20 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1340197934

Mathematical Reviews number (MathSciNet)
MR2945757

Zentralblatt MATH identifier
1260.57044

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds 57R18: Topology and geometry of orbifolds 53C27: Spin and Spin$^c$ geometry 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]

Citation

Geiges, Hansjörg; Gonzalo Pérez, Jesús. Generalised spin structures on 2-dimensional orbifolds. Osaka J. Math. 49 (2012), no. 2, 449--470. https://projecteuclid.org/euclid.ojm/1340197934


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