What is the exotic structure on R^4?

Abstract: A classical question in differential topology asks how many distinct differentiable structures exist on a certain topological manifold. Remarkably, there is a unique differentiable structure on Euclidean spaces of dimensions not equal to 4, but uncountably many on Euclidean 4-space. In this presentation, we discuss the multiple constructions for exotic structures on 4 dimensional Euclidean space, and how to produce an uncountable family of these exotic structures.

algebraic geometrycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: learners

What is ...? Seminar

Series comments: The ``What is ... ? Seminar'' (WiSe) is a weekly Zoom mathematics seminar. The goal is to explain interesting things to each other in a casual manner. The name is inspired by the What is ...? column of the Notices of the American Mathematical Society. See the website for more details. If you want to receive the zoom link for the talks please fill out the form linked on the website or contact Anna at a.puskas@uq.edu.au.