The n-Category Café

In Göttingen

Posted by Urs Schreiber

Currently the higher order structures group in Göttingen is running their reading seminar on our article L-infinity connections with Hisham Sati and Jim Stasheff. This week I am visiting Göttingen, by kind invitation by Chenchang Zhu, in order to answer questions and to speak about related structures.

Today we had a long session working our way towards the basics of synthetic differential infinity-groupoids, a context where $L_\infty$-algebras exist alongside genuine smooth $\infty$-groupoids as those who have first order infinitesimal spaces of $k$-morphisms for all $k$.

Tomorrow I’ll try to explain how using this we construct, with Domenico Fiorenza, the smooth moduli 2-stack of string 2-connections and the smooth moduli 6-stack of fivebrane 6-connections by exponentiating those big double square diagrams of $L_\infty$-algebras discussed in the article.

Today I learned from the participants that interest in the nonabelian 2-form on the 5-brane has been a motivation to pick this reading seminar topic, so I will close with a remark on the basic idea in our recent article on that application of the machinery.

Meanwhile, I am glad to have had a chance to chat with Chris Rogers about our project of studying the higher Atiyah/Courant algebroids of circle $n$-bundles for all $n$.

So it’s busy enough. Just thought I’d drop a note on what I am up to this week.