Abelian subgroups of out(Fn)

Mark Feighn, Michael Handel

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


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 into a composition of finitely many elements and then these elements are used to generate an abelian subgroup A that contains. 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.

Original languageEnglish (US)
Pages (from-to)1657-1727
Number of pages71
JournalGeometry and Topology
Issue number3
StatePublished - 2009

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


  • Free group
  • Outer automorphism
  • Train track


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