Mapping class groups of h-cobordant manifolds

Samuel Muñoz Echániz (University of Cambridge)

Monday 15th January 16:00-17:00 Maths 311B

Abstract

Given two closed h-cobordant manifolds M and M', how different can the homotopy types of the diffeomorphism groups Diff(M) and Diff(M') be? We will see that the homotopy groups of these two spaces are the same “up to extensions” in strictly positive degrees up to a range (depending on the dimension of M). Contrasting this fact, I will present examples of h-cobordant manifolds in high-dimensions with different mapping class groups. In doing so, I will introduce a moduli space of “h-block” bundles and understand its difference with the moduli space of ordinary block bundles classically analysed using surgery theory.

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