Geometry & Topology, Vol. 6 (2002) Paper no. 4, pages 69--89.

Bounded cohomology of subgroups of mapping class groups

Mladen Bestvina, Koji Fujiwara

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

AMS subject classification. Primary: 57M07, 57N05. Secondary: 57M99.

DOI: 10.2140/gt.2002.6.69

E-print: arXiv:math.GT/0012115

Submitted to GT on 15 December 2000. (Revised 28 February 2002.) Paper accepted 28 February 2002. Paper published 1 March 2002.

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Mladen Bestvina, Koji Fujiwara
Mathematics Department, University of Utah
155 South 1400 East, JWB 233
Salt Lake City, UT 84112, USA
and
Mathematics Institute, Tohoku University
Sendai, 980-8578, Japan

Email: bestvina@math.utah.edu, fujiwara@math.tohoku.ac.jp

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