#### 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 $\omega$-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