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.

Epimorphisms from 2-bridge link groups onto Heckoid groups (II)

“…This paper and its sequel [9] are concerned with the following natural question, which is an analogy of [2, Question 1.1] that is completely solved in the series of papers [3,4,5,6] and applied in [7].…”

Identities on hyperbolic manifolds

“…The identity was generalized to PSL(n, R) for Hitchin representations by Labourie and McShane in [24]. A version for two-bridge links was given by Lee and Sakuma in [26]. Recent work of Hu, Tan and Zhang in [21,22] have also given new variations and extensions of the identity to the context of Coxeter group actions on C n .…”

Canonical decompositions of hyperbolic fibered two-bridge link complements

“…In this section, we describe the 2-cell complexes dual to the canonical decompositions of hyperbolic two-bridge link complements and the induced cusp triangulations, following [13,8,11]. Let K(q/p) be a hyperbolic two-bridge link.…”