Volume 17, issue 4 (2013)

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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
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 $SL\left(2,ℂ\right)$–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
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