Unoriented cobordism categories and Klein TQFTs

Unoriented cobordism categories and Klein TQFTs

Thu, 24/05/2012
12:00 		Rosalinda Juer Junior Geometry and Topology Seminar Add to calendar L3
Unoriented cobordism categories and Klein TQFTs
The mid 1980s saw a shift in the nature of the relationship between mathematics and physics. Differential equations and geometry applied in a classical setting were no longer the principal players; in the quantum world topology and algebra had come to the fore. In this talk we discuss a method of classifying 2-dim invertible Klein topological quantum field theories (KTQFTs). A key object of study will be the unoriented cobordism category $ \mathscr{K} $, whose objects are closed 1-manifolds and whose morphisms are surfaces (a KTQFT is a functor $ \mathscr{K}\rightarrow\operatorname{Vect}_{\mathbb{C}} $). Time permitting, the open-closed version of the category will be considered, yielding some surprising results.