University of Arkansas Topology Seminar: 10/3/2019

Speaker: Jean-Pierre Mutanguha

Title: The irreducibility of monodromy is a mapping torus invariant

An immediate corollary of Nielsen-Thurston classification of surface homeomorphisms is that if two surface homeomorphisms f and g have homeomorphic mapping tori, then f is pseudo-Anosov if and only if g is pseudo-Anosov. Using hyperbolization theorem and rigidity results, the hypothesis can be weakened to quasi-isometric mapping tori. We show an analogous result for free group automorphisms: if two free group automorphisms have isomorphic mapping tori, then the first automorphism is fully irreducible and atoroidal if and only if the other is fully irreducible and atoroidal. This answers a question posed by Dowdall–Kapovich–Leininger.



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