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Michael Landry, Zoom: The veering polynomial
Monday, April 12, 2021, 02:00pm - 03:00pm
I will describe work concerning the Thurston norm on the second homology of a 3-manifold and its interaction with foliations and flows. This norm is a 3-manifold invariant with connections to many areas: geometric group theory, foliation theory, Floer theory, and more. There are some beautiful clues due to Thurston, Fried, Mosher, Gabai, McMullen, and others that indicate there should be a dictionary between the combinatorics of the norm's polyhedral unit ball and the geometric/topological structures existing in the underlying manifold. The picture is incomplete, and mostly limited to the case when the manifold fibers as a surface bundle over the circle. I will explain some new results which hold not just in the fibered case but also the more general setting of manifolds admitting veering triangulations (introduced by Agol). The main focus will be on joint work with Yair Minsky and Samuel Taylor, in which we use a veering triangulation to define a polynomial invariant which generalizes McMullen's Teichmuller polynomial.
Location: Zoom

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