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Title: McShane's identity for classical Schottky groups
Authors: Tan, S.P. 
Wong, Y.L. 
Zhang, Y.
Keywords: Fuchsian group
McShane identity
One-holed torus
Schottky group
Simple closed curve
Three-holed sphere
Weierstrass point
Issue Date: Sep-2008
Citation: Tan, S.P., Wong, Y.L., Zhang, Y. (2008-09). McShane's identity for classical Schottky groups. Pacific Journal of Mathematics 237 (1) : 183-200. ScholarBank@NUS Repository.
Abstract: In 1998, Greg McShane demonstrated a remarkable identity for the lengths of simple closed geodesics on cusped hyperbolic surfaces. In 2006, we generalized this 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, given by McShane in 2004.
Source Title: Pacific Journal of Mathematics
ISSN: 00308730
DOI: 10.2140/pjm.2008.237.183
Appears in Collections:Staff Publications

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