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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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(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 2000
Primary: 57M07, 57N05
Secondary: 57M99
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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
Mladen Bestvina
Mathematics Department
University of Utah
155 South 1400 East
JWB 233
Salt Lake City
Utah 84112
USA
Koji Fujiwara
Mathematics Institute
Tohoku University
Sendai
980-8578
Japan