Smooth structures on non-compact 4-manifolds

Isacco Nonino (University of Glasgow)

Monday 31st October, 2022 16:00-17:00 Maths 311B

Abstract

When studying smooth structures on a 4-dimensional topological manifold M, there are three main  topics one has to cover: existence, uniqueness and behavior of their diffeotopy groups. The existence and uniqueness results I will introduce will display why the 4 dimensional case is so interesting and wild, and they will also show the striking difference between the compact and non-compact settings.

I will then give an overview on the recent work on diffeotopy groups of exotic smoothings of R⁴, and show how these results were generalized to a wider class of non-compact 4 manifolds.

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