May 11th, 2021 | Colloquium
Flows, growth rates and veering triangulations
The work of Thurston, Fried, McMullen, Mosher, Fenley and others weaves together a rich picture of fibrations and flows in 3-manifolds, linking growth rates of orbits, dilatations of pseudo-Anosov maps, and Thurston's norm on homology. Agol and Gueritaud introduced veering triangulations, which are ideal triangulations associated with (certain) pseudo-Anosov flows. We use these triangulations to construct a polynomial invariant that extends McMullen's Teichmuller polynomial from suspension flows to the more general setting. We develop a combinatorial model for the flow which, with the polynomial, permits explicit computations of growth rates of orbits in naturally defined subsets of the flow. As an application we obtain, for a fibered 3-manifold, a description of the limit set of the dilatations of fibrations belonging to a fibered face of Thurston's norm. This is joint work with Michael Landry and Sam Taylor.
14:00 - Pretalk with Yair Minsky and PhD Students
14:30 - Coffee Break
14:45 - RTG colloquium