A variation of McShane’s identity for 2–bridge links

Lee, Donghi; Sakuma, Makoto

doi:10.2140/gt.2013.17.2061

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A variation of McShane's identity for 2–bridge links

Donghi Lee and Makoto Sakuma

Geometry & Topology 17 (2013) 2061–2101

DOI: 10.2140/gt.2013.17.2061

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 $SL (2, ℂ)$ –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

Volume 17, issue 4 (2013)