Joint IAS/PU Groups and Dynamics Seminar

Fibered 3-manifolds are those constructed via surface homeomorphisms. Given such a manifold with pseudo-Anosov monodromy, much is already known about how topological data of the mapping class determine geometric information about the hyperbolic 3-manifold. Currently, there is a lot of research activity surrounding the mapping tori of 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 end-periodic 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 return results to the closed, fibered setting.