Date/Time: 14 April 2023
 Location: Lebanon Valley College,
                  Clyde A. Lynch Memorial Hall, Room 182 (southeast corner of main atrium)
  Speaker: Cristy Mullican (Lebanon Valley College)
    Title: Extending Powers of Pseudo-Anosovs

 Abstract: Since surface homeomorphisms are well understood, to
study 3-manifolds with boundary we can ask, for manifold M with a
boundary component S, when does a homeomorphism of S extend to M? We can
generalize extension in the following way: A surface homeomorphism h
from S to itself partially extends to M if there is a compression body C
contained in M with exterior boundary C+=S and such that h extends to C.

In "Attaching Handlebodies to 3-manifolds" (2002) Lackenby showed
(modulo geometrization) that we can get infinitely many hyperbolic
manifolds by gluing together a simple manifold and a corresponding
handlebody via maps that don'textend to the handlebody at any power.

We will show that the power required for a pseudo-Anosov to partially
extend is not uniformly bounded; we will construct a family of
3-manifolds Mg and corresponding pseudo-Anosovs hg that require power g
to partially extend.