Topological quantum field theories for cospan cobordisms

Fiona Torzewska (University of Leeds)

Monday 4th November 16:00-17:00 Maths 311B

Abstract

The Atiyah-Segal axioms define a topological quantum field theory (TQFT) as a functor from a suitable cobordism (manifold with 'in' and 'out' boundaries) category to Vect_k, for some field k. In this talk I will introduce 'cospan cobordisms' which are certain cospans of topological spaces, and I will show how we can compose these as pushouts to construct a category. This framework is partially motivated by the more general setting it provides, for example we can include morphisms between objects of different dimension, but also because we find in some cases this is an easier category to work with to define maps into Vect_k. I will indicate how we can use cospan cobordisms to construct a TQFT given a finite group, which are a generalisation and a slight modification of those constructed by Yetter. I will also give examples to show how explicit calculation is possible.

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