A short proof of Handel and Mosher's alternative for subgroups of \(\mathrm{Out}(F_N)\). (Q2630770)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A short proof of Handel and Mosher's alternative for subgroups of \(\mathrm{Out}(F_N)\). |
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A short proof of Handel and Mosher's alternative for subgroups of \(\mathrm{Out}(F_N)\). (English)
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22 July 2016
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Summary: We give a short proof of a theorem of \textit{M. Handel} and \textit{L. Mosher} [Subgroup classification in \(\mathrm{Out}(F_n)\). Preprint (2009; \url{arXiv:0908.1255})] stating that any finitely generated subgroup of \(\mathrm{Out}(F_N)\) 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 \(\mathrm{Out}(F_N)\).
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\(\mathrm{Out}(F_N)\)
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subgroup classification
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finitely generated subgroups
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outer automorphism groups of free groups
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fully irreducible automorphisms
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