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Home » Berkeley Math Dept. Colloquiua: Dynamics and polynomial invariants of free-by-cyclic groups

Seminar

Berkeley Math Dept. Colloquiua: Dynamics and polynomial invariants of free-by-cyclic groups October 06, 2016 (04:10 PM PDT - 05:00 PM PDT)
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Location: 60 Evans Hall
Speaker(s) Ilya Kapovich (University of Illinois at Urbana-Champaign)
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The theory developed by Thurston, Fried and McMullen provides a near complete picture of the various ways a hyperbolic 3-manifold MM can fiber over the circle. Namely, there are distinguished convex cones in the first cohomology H1(M;R)H1(M;R)whose integral points all correspond to fibrations of MM, and the dynamical features of these fibrations are all encoded by McMullen's “Teichmuller polynomial." This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group GG. Specifically, we will describe a polynomial invariant that determines a convex polygonal cone CC in the first cohomology of GG whose integral points all correspond to algebraically and dynamically interesting splittings of GG. The polynomial invariant additionally provides a wealth of dynamical information about these splittings. This is a joint work with Spencer Dowdall and Christopher Leininger.

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