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G^3, Special Session in Geometric Group Theory
January 10-13, 2001
part of the AMS/MAA joint meeting
New Orleans, LA, USA

Organizers
Phil Bowers, Martin Bridson, Stephen Brick, Jon Corson, Igor Mineyev

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Translation lengths in Out(F_n)
by
Emina Alibegovic
University of Utah

Define the translation length t(g) of an element g of a group G to be

limn --> \infty |gn| / n

where G is a group with finite generating set X, and |g| denotes the length of g in the word metric on G associated with X.

Theorem: Every element O of infinite order in Out(F_n) has positive translation length. Furthermore, there exists a positive constant c_n such that t(O) >= c_n.

Consequences include a new proof that solvable subgroups of Out(F_n) are finitely generated and virtually abelian and the new result that such subgroups are quasi-convex.

Emina Alibegovic's homepage

Date received: September 28, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafm-14.