A series associated to generating pairs of a once punctured torus group and a proof of McShane’s identity

Abstract

We give a proof of McShane’s identity in "Weierstrass points and simple geodesics," Bull. London Math. Soc., 36 (2004), 181–187, based on the investigation on the arrangement of axes of simple hyperbolic elements in a once punctured torus group which are represented by palindromic words. Our argument includes a short proof of the fact that the linear measure of the infinitesimal Birman-Series set is zero.