Wed, November 10, 2021
4:10 pm - 5:40 pm
Journalism (JR) 270
Title: The geometry and topology of reflection groups
Speaker: Michael Davis
Abstract: A Coxeter group could be called an "abstract reflection group." There are two methods of realizing an abstract reflection group W as a group of symmetries of a geometric object. The first, due to Tits, is as a group generated by reflections on an open cone in some vector space. The second, due to Davis and Moussong, is as a group generated by isometric reflections on a certain cell complex (where a "cell" is a convex polytope in some Euclidean space). In both cases the underlying topological space is contractible.