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 $SL(2,\mathbb{C})$-characters of the once-punctured torus corresponding to the holonomy representations of the complete hyperbolic structures of 2-bridge link complements.

40 pages, 18 figures

References in corpus (6)

• Epimorphisms between 2-bridge link groups
• On canonical triangulations of once-punctured torus bundles and two-bridge link complements
• Generalized Markoff Maps and McShane's Identity
• Epimorphisms between 2-bridge link groups: Homotopically trivial simple loops on 2-bridge spheres
• The SL(2,C) character variety of the one-holed torus
• On hyperbolic once-punctured-torus bundles III: Comparing two tessellations of the complex plane

Cited by in corpus (2)

• McShane identities for Higher Teichmüller theory and the Goncharov-Shen potential
• Simple loops on 2-bridge spheres in Heckoid orbifolds for 2-bridge links