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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A variation of McShane's identity for 2–bridge links

Donghi Lee and Makoto Sakuma

Geometry & Topology 17 (2013) 2061–2101
Abstract

We give a variation of McShane’s identity, which describes the cusp shape of a hyperbolic 2–bridge link in terms of the complex translation lengths of simple loops on the bridge sphere. We also explicitly determine the set of end invariants of SL(2, )–characters of the once-punctured torus corresponding to the holonomy representations of the complete hyperbolic structures of 2–bridge link complements.

Dedicated to Professor Caroline Series on the occasion of her 60^th birthday

Keywords
2-bridge link, 2-bridge knot, punctured torus, end invariant, McShane's identity
Mathematical Subject Classification 2010
Primary: 20F06, 57M25, 57M50
References
Publication
Received: 27 December 2011
Revised: 25 October 2012
Accepted: 12 April 2013
Published: 18 July 2013
Proposed: Walter Neumann
Seconded: Jean-Pierre Otal, Yasha Eliashberg
Authors
Donghi Lee
Department of Mathematics
Pusan National University
Pusan 609-735
South Korea
Makoto Sakuma
Department of Mathematics
Graduate School of Science
Hiroshima University
Higashi-Hiroshima, 739-8526
Japan