Geometry MMA Seminar: Short curves of end-periodic mapping tori

Speaker:  Brandis Whitfield, Temple University

Title:  Short curves of end-periodic mapping tori

Abstract:  The mapping torus construction produces a 3-manifold from a surface homeomorphism. In the finite-type setting, much is known about how the topological data of the homeomorphism determines geometric information about the 3-manifold. Currently, there is a lot of active research activity surrounding end-periodic homeomorphisms of infinite-type surfaces.

As an "infinite type" analogue to work of Minsky in the finite-type setting, we show that given a subsurface Y of S, the subsurface projections between the "positive" and "negative" Handel-Miller laminations provide bounds for the geodesic length of the boundary of Y as it resides in the hyperbolic mapping torus.

In this talk, we'll discuss the motivating theory for finite-type surfaces and closed fibered hyperbolic 3-manifolds, show these techniques may be used in the infinite-type setting, and how our main theorems give back results to the closed, fibered setting.

Time: Monday, November 11, 2024 – 10:30am-11:30am

Place: Exploratory Hall, Room 4106