Group Theory Seminar
Mapping class groups of h-cobordant manifolds
Speaker: Samuel Muñoz-Echaniz (Cambridge)Date: Thursday, 27 March 2025 - 11:00Place: Aula Naranja, ICMAT
Abstract:
A cobordism W between compact manifolds M and M’ is an h-cobordism if the inclusions of M and M’ into W are both homotopy equivalences. This kind of cobordisms plays an important role in the classification of high-dimensional manifolds, as h-cobordant manifolds are often diffeomorphic.
With this in mind, given two h-cobordant manifolds M and M', how different can their diffeomorphism groups Diff(M) and Diff(M') be? The homotopy groups of these two spaces are the same “up to extensions” in a range of strictly positive degrees. Contrasting this fact, I will present examples of h-cobordant manifolds with different mapping class groups. In doing so, I will review the classical theory of h-cobordisms and introduce several moduli spaces of manifolds that help in answering this question.
