## Hiroshima Mathematical Journal

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

Toshihiro Nakanishi

#### 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.

#### Article information

Source
Hiroshima Math. J., Volume 41, Number 1 (2011), 11-25.

Dates
First available in Project Euclid: 31 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.hmj/1301586287

Digital Object Identifier
doi:10.32917/hmj/1301586287

Mathematical Reviews number (MathSciNet)
MR2809045

Zentralblatt MATH identifier
1233.57011

#### Citation

Nakanishi, Toshihiro. A series associated to generating pairs of a once punctured torus group and a proof of McShane’s identity. Hiroshima Math. J. 41 (2011), no. 1, 11--25. doi:10.32917/hmj/1301586287. https://projecteuclid.org/euclid.hmj/1301586287

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