Geometry & Topology

Bounded cohomology of subgroups of mapping class groups

Mladen Bestvina and Koji Fujiwara

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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
Received: 15 December 2000
Revised: 28 February 2002
Accepted: 28 February 2002
First available in Project Euclid: 21 December 2017

Permanent link to this document
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

Subjects
Primary: 57M07: Topological methods in group theory 57N05: Topology of $E^2$ , 2-manifolds
Secondary: 57M99: None of the above, but in this section

Keywords
Bounded cohomology mapping class groups hyperbolic groups

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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