Generalised spin structures on 2-dimensional orbifolds

Details Generalised spin structures on 2-dimensional orbifolds Generalised spin structures on 2-dimensional orbifolds

2010-04-12

arxiv.org/abs/1004.1979v1

Mathematics

Geometric Topology

18 pages, 3 figures

Scientific paper

Generalised spin structures, or r-spin structures, on a 2-dimensional orbifold \Sigma are r-fold fibrewise connected coverings (also called r-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 \tilde{SL}_2.

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