NONABELIAN BUNDLE 2-GERBES

Abstract

We define 2-crossed module bundle 2-gerbes related to general Lie 2-crossed modules and discuss their properties. If (L → M → N) is a Lie 2-crossed module and Y → X is a surjective submersion then an (L → M → N)-bundle 2-gerbe over X is defined in terms of a so-called (L → M → N)-bundle gerbe over the fiber product Y[2]= Y ×XY, which is an (L → M)-bundle gerbe over Y[2]equipped with a trivialization under the change of its structure crossed module from L → M to 1 → N, and which is subjected to further conditions on higher fiber products Y[3], Y[4]and Y[5]. String structures can be described and classified using 2-crossed module bundle 2-gerbes.