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G&T Monographs |
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Abelian subgroups of Out(Fn)
Mark Feighn and Michael Handel
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Geometry & Topology 13 (2009)
1657–1727
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Abstract
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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.
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Keywords
outer automorphism, free group, train
track
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Mathematical Subject Classification
Primary: 20F65
Secondary: 20F28
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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
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