Abstract
We prove that all elements of infinite order in Out(F n) have positive translation lengths; moreover, they are bounded away from zero. As a consequence we get a new proof that solvable subgroups of Out(F n) are finitely generated and virtually Abelian.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
[Bes99] Bestvina, M.: Non-positively curved aspects of artin groups of finite type, Geom. Topol. 3(3) (1999), 269–302.
[BFH99a] Bestvina, M., Feighn, M., and Handel, M.: Solvable subgroups of Out(F n ) are virtually abelian, Preprint, 1999.
[BFH99b] Bestvina, M., Feighn, M., and Handel, M.: The Tits alternative for Out(Fn) II: A Kolchin type theorem, Preprint, 1999.
[BFH00] Bestvina, M., Feighn, M., and Handel, M.: The Tits alternative for Out(Fn) I: Dynamics of exponentially growing automorphisms. Ann. of Math. 151(2) (2000), 517–623.
[BH92] Bestvina, M. and Handel, M.: Train tracks and automorphsims of free groups, Ann. of Math. (2) 135(1) (1992), 1–51.
[Coo87] Cooper, D.: Automorphisms of free groups have finitely generated fixed point sets, J. Algebra 111(2) (1987), 453–456.
[FLM] Farb, B., Lubotzky, A., and Minsky, Y.: Rank one phenomena for mapping class groups, Duke Math. J. 106(3) (2001), 581–597.
[GS91] Gersten, S. M. and Short, H. B.: Rational subgroups of automatic groups, Ann. of Math. 134 (1991), 125–158.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Alibegović, E. Translation Lengths in Out(F n). Geometriae Dedicata 92, 87–93 (2002). https://doi.org/10.1023/A:1019695003668
Issue Date:
DOI: https://doi.org/10.1023/A:1019695003668