$L^2$-torsion invariants and the Magnus representation of the mapping class group

Kitano, Teruaki; Morifuji, Takayuki

doi:10.2969/aspm/05210031

VOL. 52 | 2008 $L^2$-torsion invariants and the Magnus representation of the mapping class group

Chapter Author(s) Teruaki Kitano, Takayuki Morifuji

Editor(s) Robert Penner, Dieter Kotschick, Takashi Tsuboi, Nariya Kawazumi, Teruaki Kitano, Yoshihiko Mitsumatsu

Adv. Stud. Pure Math., 2008: 31-49 (2008) DOI: 10.2969/aspm/05210031

Abstract

In this paper, we study a series of $L^2$-torsion invariants from the viewpoint of the mapping class group of a surface. We establish some vanishing theorems for them. Moreover we explicitly calculate the first two invariants and compare them with hyperbolic volumes.