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On a theorem by Farb and Masur

Author(s): Koji Fujiwara
Journal: Proc. Amer. Math. Soc. 128 (2000), 3463-3464.
MSC (1991): Primary 20F32; Secondary 20F34, 22E40, 32G15
Posted: June 7, 2000
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Abstract:

Farb and Masur showed that an irreducible lattice in a semisimple Lie group of rank at least two always has finite image by a homomorphism into the outer automorphism group of a closed, orientable surface group. We point out that their theorem extends to the outer automorphism groups of a certain class of torsion-free, freely indecomposable word-hyperbolic groups.

References:

[BH]: J. Birman, H. Hilden, On isotopies of homeomorphisms of Riemann surfaces. Ann. of Math. (2) 97 (1973), 424-439. MR 48:4305
[FM]: B. Farb, H. Masur, Superrigidity and mapping class groups, Topology. 37 (1998), No. 6, 1169-1176. MR 99f:57017
[G]: M. Gromov, Hyperbolic groups. Essays in group theory, 75-263, MSRI Publ. 8, Springer, 1987. MR 89e:20070
[I]: N. V. Ivanov, Algebraic properties of mapping class groups of surfaces. Geometric and algebraic topology, 15-35, Banach Center Publ. 18, PWN, Warsaw, 1986. MR 89a:57009
[KM]: V. A. Kaimanovich, H. Masur, The Poisson boundary of the mapping class group. Invent. Math. 125 (1996), No. 2, 221-264. MR 97m:32033
[S]: Z. Sela, Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank Lie groups. II. Geom. Funct. Anal. 7 (1997), No. 3, 561-593. MR 98j:20044

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Additional Information:

Koji Fujiwara
Affiliation: Mathematical Institute, Tohoku University, Sendai, 980-8578 Japan
Email: fujiwara@math.tohoku.ac.jp

DOI: 10.1090/S0002-9939-00-05450-2
PII: S 0002-9939(00)05450-2
Keywords: Word-hyperbolic groups, JSJ-decomposition, lattices in higher-rank Lie groups, mapping class groups
Received by editor(s): December 11, 1998
Received by editor(s) in revised form: February 8, 1999
Posted: June 7, 2000
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 2000, American Mathematical Society


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