## Geometry & Topology

### Bounded cohomology of subgroups of mapping class groups

#### Abstract

We show that every subgroup of the mapping class group $MCG(S)$ 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 $MCG(S)$ does not contain a higher rank lattice as a subgroup.

#### Article information

Source
Geom. Topol., Volume 6, Number 1 (2002), 69-89.

Dates
Revised: 28 February 2002
Accepted: 28 February 2002
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513882790

Digital Object Identifier
doi:10.2140/gt.2002.6.69

Mathematical Reviews number (MathSciNet)
MR1914565

Zentralblatt MATH identifier
1021.57001

#### Citation

Bestvina, Mladen; Fujiwara, Koji. Bounded cohomology of subgroups of mapping class groups. Geom. Topol. 6 (2002), no. 1, 69--89. doi:10.2140/gt.2002.6.69. https://projecteuclid.org/euclid.gt/1513882790

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