Mathematical Research Letters

Volume 22 (2015)

Number 2

A new identity for $\textrm{SL}(2,\mathbf{C})$-characters of the once punctured torus group

Pages: 485 – 499

DOI: https://dx.doi.org/10.4310/MRL.2015.v22.n2.a8

Authors

Hengnan Hu (Department of Mathematics, National University of Singapore)

Ser Peow Tan (Department of Mathematics, National University of Singapore)

Ying Zhang (School of Mathematical Sciences, Soochow University, Suzhou, China)

Abstract

We obtain new variations of the original McShane identity for those $\textrm{SL}(2,\mathbf{C})$–representations of the once punctured torus group which satisfy the Bowditch conditions, and also for those fixed up to conjugacy by an Anosov mapping class of the torus and satisfying the relative Bowditch conditions.

Keywords

McShane identity, Markoff map, once-punctured torus, simple closed geodesics

2010 Mathematics Subject Classification

20H10, 30F60, 37F30, 53C22, 57M05

Full Text (PDF format)

Accepted 8 July 2014

Published 16 April 2015