Compactifications of Manifolds with Boundary

Shijie Gu
University of Wisconsin-Milwaukee
PhD Graduate Student

“This dissertation is about compactifications of manifolds. The “nicest” of these compactifications is the addition of a boundary to an open manifold (or to a manifold with compact boundary). That was the topic of Siebenmann’s famous 1965 dissertation. When a manifold M has noncompact boundary, one seeks a compactification which completes the boundary of M . That is a more delicate problem. Siebenmann addressed a very special case in his 1965 dissertation and O’Brien extended that work to cases where M and boundary of M are both 1-ended. We will present a full characterization, thereby completing an unfinished chapter in the study of noncompact manifolds. As a natural generalization, we obtain a complete characterization of pseudo-collarable manifolds. Meanwhile, we explore some new results about Z-compactifications of manifolds.”

Committee Members:
Profs. Craig Guilbault (Advisor), Suzanne Boyd, Peter Hinow, Chris Hruska & Boris Okun