Bounded cohomology of subgroups of mapping class groups

Bestvina, Mladen¹ ; Fujiwara, Koji²

¹ Mathematics Department, University of Utah, 155 South 1400 East, JWB 233, Salt Lake City, Utah 84112, USA
² Mathematics Institute, Tohoku University, Sendai, 980-8578, Japan

Geometry & topology, Tome 6 (2002) no. 1, pp. 69-89.

Résumé

We show that every subgroup of the mapping class group $MCG\left(S\right)$ of a compact surface $S$ is either virtually abelian or it has infinite dimensional second bounded cohomology. As an application, we give another proof of the Farb–Kaimanovich–Masur rigidity theorem that states that $MCG\left(S\right)$ does not contain a higher rank lattice as a subgroup.

Détail

DOI : 10.2140/gt.2002.6.69

Keywords: Bounded cohomology, mapping class groups, hyperbolic groups

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