A McShane-type identity for closed surfaces
arXiv:1203.3860
Abstract
We prove a McShane-type identity - a series, expressed in terms of geodesic lengths, that sums to 2πfor any closed hyperbolic surface with one distinguished point. To do so, we prove a generalized Birman-Series theorem showing that the set of complete geodesics on a hyperbolic surface with large cone angles is sparse.
V3: 18 pages, 11 figures, presented at the 56th annual AustMS meeting. Fixed over-counting error. V2: Paper was withdrawn due to an error in lemma 9. V1: 12 pages, 4 figures, results presented at the "Geometry and Arithmetic around Teichmueller Theory" at Galatasaray University in 2011