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Abelian subgroups of Out(Fn)

Mark Feighn and Michael Handel

Geometry & Topology 13 (2009) 1657–1727

DOI: 10.2140/gt.2009.13.1657
Abstract

We classify abelian subgroups of Out(Fn) up to finite index in an algorithmic and computationally friendly way. A process called disintegration is used to canonically decompose a single rotationless element ϕ into a composition of finitely many elements and then these elements are used to generate an abelian subgroup A(ϕ) that contains ϕ. The main theorem is that up to finite index every abelian subgroup is realized by this construction. As an application we give an explicit description, in terms of relative train track maps and up to finite index, of all maximal rank abelian subgroups of Out(Fn) and of IAn.

Keywords

outer automorphism, free group, train track
Mathematical Subject Classification

Primary: 20F65

Secondary: 20F28
References
Publication

Received: 21 February 2007
Revised: 25 February 2009
Accepted: 7 March 2008
Published: 5 March 2009
Proposed: Benson Farb
Seconded: Martin Bridson, Joan Birman
Authors
Mark Feighn
Math Department
Rutgers University
Newark, NJ 07102
USA
Michael Handel
Math Department
Lehman College
Bronx, NY 10468
USA