### Cobordism and Topological Field Theories Weeks 6 & 7

#### Posted by Alexander Hoffnung

Welcome back to the cobordism and TFT seminar at UCR! We are posting weeks 6 and 7 of the seminar simultaneously because it flows nicely and the new quarter will start before we know it. So we want to be all caught up by the first week of the second quarter.

Week 6 starts back with the regular lecture series by Julie Bergner. These lectures are especially nice as they begin to introduce $n$-dimensional topological field theories in Lecture 6 and the higher category theory needed to formulate these concepts in Lecture 7.

You can click here for the previous week’s lecture and keep reading below the fold for a link to the notes for Weeks 6 and 7…

In Lecture 6, Julie reminds us of some of facts about $2$-dimensional topological field theories stated in Chris Carlson’s lecture in Week 4. She comes to a sketch of a $2$-extended TFT by chopping up manifolds into pieces and considering the problems encountered when one considers TFT’s of dimension higher than 2.

Following the realization that we no longer have a symmetric monoidal category of cobordisms, in Lecture 7, Julie then introduces $2$-categories of cobordisms. She then hints at the coming need for $(\infty,2)$-categories and gives a definition for extended $\mathcal{C}$-valued TFT’s.

Here are the lecture notes for Weeks 6 and 7.

Next week, John Baez will fill in some details regarding symmetric monoidal weak $2$-categories…

## Re: Cobordism and Topological Field Theories Weeks 6 & 7

It is a very minor point, but I suggest that the arrows labeled “left” be put into mboxes.