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2-vector bundles

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arxiv 2106.12198 v2 pith:HRKPPRSZ submitted 2021-06-23 math.DG math.ATmath.RA

Peter Kristel , Matthias Ludewig , Konrad Waldorf This is my paper · ORCID
classification math.DGmath.ATmath.RA
keywords bundlesvectoralgebrabundlegerbessupertheoryalgebras
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We develop a ready-to-use comprehensive theory for (super) 2-vector bundles over smooth manifolds. It is based on the bicategory of (super) algebras, bimodules, and intertwiners as a model for 2-vector spaces. We discuss symmetric monoidal structures and the corresponding notions of dualizability, and we derive a classification in terms of Cech cohomology with values in a crossed module. One important feature of our 2-vector bundles is that they contain bundle gerbes as well as ordinary algebra bundles as full sub-bicategories, and hence provide a unifying framework for these so far distinct objects. We provide several examples of isomorphisms between bundle gerbes and algebra bundles, coming from representation theory, twisted K-theory, and spin geometry.

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Cited by 3 Pith papers

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    hep-th 2025-06 conditional novelty 7.0 of 10

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    math.AT 2026-01 reject novelty 6.0 of 10

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