### Higher Structures in Topology and Geometry V

#### Posted by Urs Schreiber

*guest post by Christoph Wockel*

Dear all:

We cordially invite you to participate in the workshop *Higher Structures in Topology and Geometry V* , which will take place May 25-27 in Hamburg (Germany). For information about speakers and location, you may consult our webpage:

• *Higher Structures in Topology and Geometry V*.

Best wishes,

Christoph Wockel (on behalf of the organisers Christoph Schweigert, Giorgio Trentinaglia and Chenchang Zhu)

Posted at January 31, 2011 1:39 PM UTC
## Chris Schommer-Pries on fusion categories and TQFT

I have only just arrived, by night train over the Alps from

Venezia. Am a bit tired. But now Chris Schommer-Pries is talking about a nice result that he told me about a few weeks back in Lisbon.I don’t think there is anything in print, but the abstract on his webpage is slightly more detailed than the talk abstract:

So the idea is: there are plenty of component-based constructions in the literature that produce 3-dimensional TQFTs from the data of a fusion category. So far no particularly deeper reason for

whyall these constructions exist for fusion categories has been known. The theorem now says: simply because fusion categories are, in their natural ambient 3-category, fully dualizable objects: precisely the kind of objects that the general abstract cobordism hypothesis says arise as the value of extended QFTs on the point and indeed fully characterize these extended QFTs.More is true: there are slight variants of the cobordism hypothesis, depending on which extra topological structure the cobordisms are equipped with, for instance: framing, or orientation. There are also variants of notions of fusion categories equipped with extra property and structure: pivotal categories and spherical categories (though there is a conjecture saying that these are all the same). Chris et al.’s theorem says that under the above correspondence, these extra structures match on both sides.

In a little while, more details are here.