
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.
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