Nonabelian bundle 2-gerbes

TL;DR

This paper introduces 2-crossed module bundle 2-gerbes, a new mathematical framework for describing and classifying string structures using advanced concepts in Lie 2-crossed modules.

Contribution

It defines 2-crossed module bundle 2-gerbes related to Lie 2-crossed modules and demonstrates their application in classifying string structures.

Findings

Defined 2-crossed module bundle 2-gerbes over manifolds.

Connected 2-crossed module bundle 2-gerbes to string structures.

Provided a classification framework for string structures.

Abstract

We define 2-crossed module bundle 2-gerbes related to general Lie 2-crossed modules and discuss their properties. A 2-crossed module bundle 2-gerbe over a manifold is defined in terms of a so called 2-crossed module bundle gerbe, which is a crossed module bundle gerbe equipped with an extra sructure. It is shown that string structures can be described and classified using 2-crossed module bundle 2-gerbes.