Stable commutator length on mapping class groups

By M. Bestvina, K. Bromberg, K. Fujiwara. 2013

57 citations recorded by the source corpus.

Let $\Gamma$ be a finite index subgroup of the mapping class group $MCG(\Sigma)$ of a closed orientable surface $\Sigma$, possibly with punctures. We give a precise condition (in terms of the Nielsen-Thurston decomposition) when an element $g\in\Gamma$ has positive stable commutator length. In addition, we show that in these situations the stable commutator length, if nonzero, is uniformly bounded away from 0. The method works for certain subgroups of infinite index as well and we show $scl$ is uniformly positive on the nontrivial elements of the Torelli group. The proofs use our earlier construction in the paper "Constructing group actions on quasi-trees and applications to mapping class groups" of group actions on quasi-trees.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b308785e1341557c85c970835bfa17f9b51e9db5

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In Geometry and Topology

1. Juliette Bavard
2. Nicholas G. Vlamis
3. Priyam Patel

In Mathematical Physics

1. Juliette Bavard
2. Nicholas G. Vlamis
3. Priyam Patel

Citations in the corpus

• Gromov-Hyperbolicity of the ray graph and quasimorphisms on a big mapping class group (2014, background): “Dans le cas des surfaces de type fini, on sait maintenant caractériser précisément en termes de la décomposition de Nielsen–Thurston les éléments de scl nulle (voir Bestvina, Bromberg et Fujiwara [4]).”