On a theorem by Farb and Masur
HTML articles powered by AMS MathViewer
- by Koji Fujiwara PDF
- Proc. Amer. Math. Soc. 128 (2000), 3463-3464 Request permission
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
- Joan S. Birman and Hugh M. Hilden, On isotopies of homeomorphisms of Riemann surfaces, Ann. of Math. (2) 97 (1973), 424–439. MR 325959, DOI 10.2307/1970830
- Benson Farb and Howard Masur, Superrigidity and mapping class groups, Topology 37 (1998), no. 6, 1169–1176. MR 1632912, DOI 10.1016/S0040-9383(97)00099-2
- M. Gromov, Hyperbolic groups, Essays in group theory, Math. Sci. Res. Inst. Publ., vol. 8, Springer, New York, 1987, pp. 75–263. MR 919829, DOI 10.1007/978-1-4613-9586-7_{3}
- N. V. Ivanov, Algebraic properties of mapping class groups of surfaces, Geometric and algebraic topology, Banach Center Publ., vol. 18, PWN, Warsaw, 1986, pp. 15–35. MR 925854
- Vadim A. Kaimanovich and Howard Masur, The Poisson boundary of the mapping class group, Invent. Math. 125 (1996), no. 2, 221–264. MR 1395719, DOI 10.1007/s002220050074
- Z. Sela, Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank $1$ Lie groups. II, Geom. Funct. Anal. 7 (1997), no. 3, 561–593. MR 1466338, DOI 10.1007/s000390050019
Additional Information
- Koji Fujiwara
- Affiliation: Mathematical Institute, Tohoku University, Sendai, 980-8578 Japan
- MR Author ID: 267217
- Email: fujiwara@math.tohoku.ac.jp
- Received by editor(s): December 11, 1998
- Received by editor(s) in revised form: February 8, 1999
- Published electronically: June 7, 2000
- Communicated by: Ronald A. Fintushel
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3463-3464
- MSC (1991): Primary 20F32; Secondary 20F34, 22E40, 32G15
- DOI: https://doi.org/10.1090/S0002-9939-00-05450-2
- MathSciNet review: 1690987