Vol. 272, No. 2, 2014

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On stable commutator length in hyperelliptic mapping class groups

Danny Calegari, Naoyuki Monden and Masatoshi Sato

Vol. 272 (2014), No. 2, 323–351
Abstract

We give a new upper bound on the stable commutator length of Dehn twists in hyperelliptic mapping class groups and determine the stable commutator length of some elements. We also calculate values and the defects of homogeneous quasimorphisms derived from ω-signatures and show that they are linearly independent in the mapping class groups of pointed 2-spheres when the number of points is small.

Keywords
stable commutator length, mapping class groups
Mathematical Subject Classification 2010
Primary: 57M07
Secondary: 20F12, 57N05
Milestones
Received: 23 August 2013
Revised: 28 February 2014
Accepted: 7 April 2014
Published: 28 November 2014
Authors
Danny Calegari
Department of Mathematics
University of Chicago
5734 South University Avenue
Chicago, IL 60637
United States
Naoyuki Monden
Department of Engineering Science
Osaka Electro-Communication University
Hatsu-cho 18-8
Neyagawa 572-8530
Japan
Masatoshi Sato
Department of Mathematics Education
Gifu University
Yanagito 1-1
Gifu 501-1193
Japan