Geometry & Topology

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

Donghi Lee and Makoto Sakuma

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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.

Article information

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

Dates
Received: 27 December 2011
Revised: 25 October 2012
Accepted: 12 April 2013
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Subjects
Primary: 20F06: Cancellation theory; application of van Kampen diagrams [See also 57M05] 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M50: Geometric structures on low-dimensional manifolds

Keywords
2-bridge link 2-bridge knot punctured torus end invariant McShane's identity

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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