Subgroup classification in Out(F_n)

2009/08/09 by Michael Handel, Lee Mosher, Handel, Michael +1
Computer Science · Mathematics · #20F65 57M07 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.CT #math.GR #msc:20F65 #msc:57M07 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0908.1255

83 pages

arxiv created 2009/08/09 · openalex publication_date 2009/08/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any subgroup H of Out(F_n), either H has a finite index subgroup that fixes the conjugacy class of some proper, nontrivial free factor of F_n, or H contains a fully irreducible element phi, meaning that no positive power of phi fixes the conjugacy class of any proper, nontrivial free factor of F_n.

Citations

• A hyperbolic Out(F_n)-complex

Related

• A short proof of Handel and Mosher's alternative for subgroups of Out(F_N)
• Subgroup decomposition in \Out(F_n), Part IV: Relatively\n irreducible subgroups
• A McCool Whitehead type theorem for finitely generated subgroups of Out(F_n)
• Counting conjugacy classes of subgroups in a finitely generated group
• The conjugacy problem in Out(Fm) when the polynomial restrictions are non-growing