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Institute of Algebra and Geometry
Research Group Algebraic and Geometric Topology
AG Algebraic und Geometric Topology

Samuel Muñoz-Echániz

Title:Mapping class groups of h-cobordant manifolds
Speaker:Samuel Muñoz-Echániz
Time:Thursday, 17.07.2025, 14:30
Place:SR 3.69

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.