Caltech/USC Joint Algebra and Geometry Seminar

Let k be an algebraically closed field of characteristic zero. It is well known that oriented 2-dimensional cobordisms recover the Deligne category Rep(St), which interpolates the category of finite-dimensional representations of the symmetric group Sn from natural numbers n to an arbitrary parameter t in k. In this talk, we review this construction and show that an analogous story holds in the unoriented case: unoriented 2-dimensional cobordisms recover the generalized Deligne category Rep(St wreath Z2).