Stable length in stable groups

Kotschick, Dieter

doi:10.2969/aspm/05210401

VOL. 52 | 2008 Stable length in stable groups

Dieter Kotschick

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

Adv. Stud. Pure Math., 2008: 401-413 (2008) DOI: 10.2969/aspm/05210401

Abstract

We show that the stable commutator length vanishes for certain groups defined as infinite unions of smaller groups. The argument uses a group-theoretic analogue of the Mazur swindle, and goes back to the works of Anderson, Fisher, and Mather on homeomorphism groups.