On stable commutator length in hyperelliptic mapping class groups

Danny Calegari, Naoyuki Monden and Masatoshi Sato

Vol. 272 (2014), No. 2, 323–351

DOI: 10.2140/pjm.2014.272.323

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