Carmen Rovi : Topology meets Physics: Scissors Congruences and TQFTs.

Posted by Laura Schaposnik , part of the Departmental Colloquium.

At

Feb. 23, 2024, 3 p.m.

In

636 SEO

Abstract

In this talk, we will be concerned with a relation between TQFTs and the controlled cut-and-paste invariants of manifolds introduced by Karras, Kreck, Neumann, and Ossa. The controlled cut-and-paste invariants (SKK invariants) are functions on the set of smooth manifolds whose values on cut-and-paste equivalent manifolds differ by an error term depending only on the gluing diffeomorphisms. I will present a natural group homomorphism between the group of invertible TQFTs and the group of SKK invariants and describe how these groups fit into a split exact sequence. We conclude in particular that all positive real-valued SKK invariants can be realized as restrictions of invertible TQFTs.

There will be a dinner at 7:15 that evening please email schapos@uic.edu if you'd like to join