Geometric Analysis and Topology Seminar

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Fibrations, Subsurface Projections and Veering Triangulations

Speaker: Yair Minsky, Yale

Location: Warren Weaver Hall 517

Date: Friday, November 4, 2016, 11 a.m.

Synopsis:

When a hyperbolic 3-manifold fibers over the circle, its geometric features can be read from the fine structure of its monodromy map, specifically the "subsurface projections" of the stable and unstable foliations to the arc complexes of subsurfaces of the fiber. While this correspondence is useful when the topological type of the fiber is fixed, it is not well-understood in general. A good laboratory for studying this is a single 3-manifold that fibers in infinitely many different ways, as organized by Thurston's norm on homology. In this setting there are canonical triangulations due to Agol, which can be studied very explicitly via a construction of Gueritaud. We explore how the subsurface projections of monodromies for all the fibers can be seen in the structure of this triangulation, and how this leads to a nice combinatorial picture with estimates that do not depend on complexity of the fibers. Joint work with Sam Taylor.