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.