A short proof of Handel and Mosher's alternative for subgroups of Out(F_N)

2014/04/17 by Camille Horbez, Horbez, Camille
Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1404.4626

openalex publication_date 2014/04/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We give a short proof of a theorem of Handel and Mosher stating that any finitely generated subgroup of Out(F_N) either contains a fully irreducible automorphism, or virtually fixes the conjugacy class of a proper free factor of F_N, and we extend their result to non finitely generated subgroups of Out(F_N).

Citations

• Subgroup decomposition in Out(F_n): Introduction and Research Announcement

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• Subgroup decomposition in \Out(F_n), Part IV: Relatively\n irreducible subgroups
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