Subgroup classification in Out(F_n)
Michael Handel, Lee Mosher
TL;DR
This paper classifies subgroups of Out(F_n) into those that contain fully irreducible elements and those that virtually fix a proper free factor, providing a clear dichotomy in subgroup structure.
Contribution
It establishes a subgroup classification theorem for Out(F_n), distinguishing between virtually fixing free factors and containing fully irreducible elements.
Findings
Subgroups either contain a fully irreducible element or virtually fix a free factor.
The classification provides a structural understanding of subgroups in Out(F_n).
The result parallels similar dichotomies in mapping class groups.
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.
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Taxonomy
TopicsGeometric and Algebraic Topology · semigroups and automata theory · Algebraic structures and combinatorial models