## Geometry & Topology

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

#### 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.

#### Article information

Source
Geom. Topol., Volume 17, Number 4 (2013), 2061-2101.

Dates
Revised: 25 October 2012
Accepted: 12 April 2013
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513732647

Digital Object Identifier
doi:10.2140/gt.2013.17.2061

Mathematical Reviews number (MathSciNet)
MR3109863

Zentralblatt MATH identifier
1311.57022

#### Citation

Lee, Donghi; Sakuma, Makoto. A variation of McShane's identity for 2–bridge links. Geom. Topol. 17 (2013), no. 4, 2061--2101. doi:10.2140/gt.2013.17.2061. https://projecteuclid.org/euclid.gt/1513732647

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