McShane's identity for classical Schottky Groups
Geometric Topology
2007-05-23 v1 Differential Geometry
Abstract
Greg McShane introduced a remarkable identity for the lengths of simple closed geodesics on cusped hyperbolic surfaces. This was subsequently generalized by the authors to hyperbolic cone-surfaces, possibly with cusps and/or geodesic boundary. In this paper, we generalize the identity further to the case of classical Schottky groups. As a consequence, we obtain some surprising new identities in the case of fuchsian Schottky groups. For classical Schottky groups of rank 2, we also give generalizations of the Weierstrass identities, first given by McShane.
Cite
@article{arxiv.math/0411628,
title = {McShane's identity for classical Schottky Groups},
author = {Ser Peow Tan and Yan Loi Wong and Ying Zhang},
journal= {arXiv preprint arXiv:math/0411628},
year = {2007}
}
Comments
14 pages, 2 figures