LisMath Seminar 

13/07/2023, 11:30 — 12:00 — Online
Arber Selimi, Instituto Superior Técnico, Universidade de Lisboa

Categorical aspects of 3-Bundles and 3-connections

The subject of principal bundles with connections (gauge theory) and their higher versions are of special interest in mathematics and physics. Using the known strategies of constructing non abelian bundle gerbes using the plus construction, we give meaning to the tricategory of nonabelian 2-crossed module 2-bundle gerbes using a higher notion of the plus construction. We will view nonabelian 2-crossed module 2-bundle gerbes also as bigroupoids with a 3-group action, and we call them principal 3-bundles. Also we will describe the cocycle conditions, and the classifying space of a 2-crossed module, which will allow us to see isomorphism classes of principal 3-bundles over a smooth manifold $X$ as homotopy classes of classifying maps from $X$ to the classifying space of the 2-crossed module. In the final part we will also discuss 3-connections, where we will compare two different definitions of holonomies for flat 3-connections.