2006/12/22 by Mark Feighn, Michael Handel
Mathematics · #Abelian group #Advanced Topology and Set Theory #Composition (language) #Elementary abelian group #Finite Group Theory Research #Geometric and Algebraic Topology #Locally finite group #Omega and agemo subgroup #Rank (graph theory) #Rank of an abelian group #Torsion subgroup #math.GR #msc:20F28 #msc:20F65
paper · pdf · doi:10.2140/gt.2009.13.1657
published as Geom. Topol. 13 (2009) 1657-1727 · 56 pages
arxiv created 2006/12/22 · openalex publication_date 2009/03/05 · arxiv updated 2014/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We classify abelian subgroups of Out.F n / 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.F n / and of IA n .