Atoroidal dynamics of subgroups of Out(F_N)

Matt Clay; Caglar Uyanik

doi:10.1112/jlms.12339

Atoroidal dynamics of subgroups of Out(F_N)

Group Theory 2024-06-14 v3 Geometric Topology

Authors: Matt Clay , Caglar Uyanik

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Abstract

We show that for any subgroup $H$ of Out( $F_N$ ), either $H$ contains an atoroidal element or a finite index subgroup $H'$ 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.

Keywords

out(f_n) subgroup theorem atoroidal element conjugacy class mapping class group irreducible element

Cite

@article{arxiv.1901.02071,
  title  = {Atoroidal dynamics of subgroups of Out(F_N)},
  author = {Matt Clay and Caglar Uyanik},
  journal= {arXiv preprint arXiv:1901.02071},
  year   = {2024}
}

Comments

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

Atoroidal dynamics of subgroups of Out(F_N)

Abstract

Keywords

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