Free group automorphisms with many fixed points at infinity

Details Free group automorphisms with many fixed points at infinity Free group automorphisms with many fixed points at infinity

2009-04-09

arxiv.org/abs/0904.1533v1

Geom. Topol. Monogr. 14 (2008) 321-333

Mathematics

Group Theory

This is the version published by Geometry & Topology Monographs on 29 April 2008

Scientific paper

10.2140/gtm.2008.14.321

A concrete family of automorphisms alpha_n of the free group F_n is exhibited, for any n > 2, and the following properties are proved: alpha_n is irreducible with irreducible powers, has trivial fixed subgroup, and has 2n-1 attractive as well as 2n repelling fixed points at bdry F_n. As a consequence of a recent result of V Guirardel there can not be more fixed points on bdry F_n, so that this family provides the answer to a question posed by G Levitt.

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