Geometry & Topology 6 (2002) 69–89

DOI: 10.2140/gt.2002.6.69

arXiv: math.GT/0012115

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.

Keywords

Bounded cohomology, mapping class groups, hyperbolic groups

Mathematical Subject Classification

Primary: 57M07, 57N05

Secondary: 57M99

References

Forward citations

Publication

Received: 15 December 2000
Revised: 28 February 2002
Accepted: 28 February 2002
Published: 1 March 2002
Proposed: Joan Birman
Seconded: Dieter Kotschick, Steven Ferry

Authors