{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:KHIMZR7EI4K4P5JSUQB5FA4HZF","short_pith_number":"pith:KHIMZR7E","schema_version":"1.0","canonical_sha256":"51d0ccc7e44715c7f532a403d28387c962a661f6b96bd2639a82c616b520fb82","source":{"kind":"arxiv","id":"0904.1881","version":3},"attestation_state":"computed","paper":{"title":"Stabilizers of $\\mathbb R$-trees with free isometric actions of $F_N$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Ilya Kapovich, Martin Lustig","submitted_at":"2009-04-12T19:27:23Z","abstract_excerpt":"We prove that if $T$ is an $\\mathbb R$-tree with a minimal free isometric action of $F_N$, then the $Out(F_N)$-stabilizer of the projective class $[T]$ is virtually cyclic.\n  For the special case where $T=T_+(\\phi)$ is the forward limit tree of an atoroidal iwip element $\\phi\\in Out(F_N)$ this is a consequence of the results of Bestvina, Feighn and Handel, via very different methods.\n  We also derive a new proof of the Tits alternative for subgroups of $Out(F_N)$ containing an iwip (not necessarily atoroidal): we prove that every such subgroup $G\\le Out(F_N)$ is either virtually cyclic or 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