Generalized duality structures and ansular functors

For zoom details contact Peter Teichner (teichner@mpim-bonn.mpg.de) or
David Reutter.

    Rigid monoidal categories play a prominent role in quantum algebra and quantum topology. However, rigidity imposes strong restrictions. For example, it implies that the tensor product is exact.  Examples from the representation theory of vertex operator algebras with non-exact tensor products show the need for a weaker notion of duality for the categorical description of non-rational conformal field theories.
    In my talk, I will discuss Grothendieck-Verdier duality as defined by Boyarchenko-Drinfeld as a potential solution to these problems. I will focus on the connection to topology, in particular the mapping class groups of three-dimensional handlebodies, the so-called handlebody groups. More precisely, I will prove that consistent systems of handlebody group representations (so-called ansular functors) are equivalent to ribbon Grothendieck-Verdier categories. The talk is based on joint work with Lukas Woike.