Rigid models for 2-gerbes I: Chern–Simons geometry
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(Embargo ends 18 February 2027)
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2026
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Roberts, D.M.
Vozzo, R.F.
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Journal of Homotopy and Related Structures, 2026; 1-66
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David Michael Roberts, Raymond F. Vozzo
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Motivated by the problem of constructing explicit geometric string structures, we give a rigid model for bundle 2-gerbes, and define connective structures thereon. This model is designed to make explicit calculations easier in applications to physics. To compare to the existing definition, we give a functorial construction of a bundle 2-gerbe as in the literature from our rigid model, including with connections. As an example we prove that the Chern–Simons bundle 2-gerbe from the literature, with its connective structure, can be rigidified—it arises, up to isomorphism in the strongest possible sense, from a rigid bundle 2-gerbe with connective structure via this construction. Further, our rigid version of 2-gerbe trivialisation (with connections) gives rise to trivialisations (with connections) of bundle 2-gerbes in the usual sense, and as such can be used to describe geometric string structures. The preprint of this article is available as arXiv:2209.05521.
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© The Author(s), under exclusive licence to Tbilisi Centre for Mathematical Sciences 2026