Atoroidal dynamics of subgroups of Out(F_N)

Abstract

We show that for any subgroup $H$ of Out($F_N$), either $H$ contains an atoroidal element or a finite index subgroup $H^{\prime }$ of $H$ fixes a nontrivial conjugacy class in $F_N$. This result is an analog of Ivanov's subgroup theorem for mapping class groups and Handel-Mosher's subgroup theorem for Out($F_N$) in the setting of irreducible elements.

38 pages, 2 figures; v2: new result added, updated references; v3: final version, incorporate changes suggested by referee, to appear in the Journal of the LMS

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• The co-surface graph and the geometry of hyperbolic free group extensions
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Cited by in corpus (1)

• Boundaries of relative factor graphs and subgroup classification for automorphisms of free products