McShane's identity for classical Schottky Groups

Details McShane's identity for classical Schottky Groups McShane's identity for classical Schottky Groups

2004-11-29

arxiv.org/abs/math/0411628v1

Mathematics

Geometric Topology

14 pages, 2 figures

Scientific paper

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.

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