Matt Foreman : Classifying the qualitative behavior of smooth transformations using descriptive set theory

Posted by Filippo Calderoni , part of the Logic Seminar.

At

March 15, 2022, 4 p.m.

In

636 SEO

Abstract

In 1967 Smale proposed classifying the "qualitative behavior” of diffeomorphisms of compact smooth manifolds. Despite very significant activity, the general problem remained open. However joint work with Gorodetski shows that in dimensions 2 and above, there are no complete invariants and in dimension 5 and above the equivalence relation is not even Borel. Hence there can be no classification using inherently countable information.