#### Volume 6, issue 1 (2002)

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Bounded cohomology of subgroups of mapping class groups

### Mladen Bestvina and Koji Fujiwara

Geometry & Topology 6 (2002) 69–89
 arXiv: math.GT/0012115
##### Abstract

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.

##### Keywords
Bounded cohomology, mapping class groups, hyperbolic groups
##### Mathematical Subject Classification 2000
Primary: 57M07, 57N05
Secondary: 57M99