Compactifications of manifolds with boundary
Shijie Gu (Central Connecticut State University)
Location: Hill 705
Date & time: Tuesday, 19 November 2019 at 3:50PM - 4:40PM
Abstract: In 1966, Larry Siebenmann once mused that his work (PhD thesis) was initiated at a time "when 'respectable' geometric topology was necessarily compact". That attitude has long since faded; today's topological landscape is filled with research in which noncompact spaces are primary objects. However, major successes in understanding and compactifiying certain noncompact spaces included here are fundamental to manifold topology and geometric group theory: Whitehead and Davis manifolds, Stalling's characterization of Euclidean spaces, Siebenmann's thesis and our recent Gu-Guilbault's manifold completion theorem --- to name just a few. My goal is to provide a quick access to some of those results by weaving them together with common interpretations, motivating examples and my current research.
I hope this talk will give the audience with various interests a brief appreciation of some of that work.