| Title:
|
2-vector bundles (English) |
| Author:
|
Waldorf, Konrad |
| Author:
|
Kristel, Peter |
| Author:
|
Ludewig, Matthias |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
9 |
| Issue:
|
1 |
| Year:
|
2025 |
| Pages:
|
36-87 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Super algebras |
| Keyword:
|
bimodules |
| Keyword:
|
bundle gerbes |
| Keyword:
|
bicategories |
| Keyword:
|
Morita equivalence |
| Keyword:
|
2 Stacks |
| Keyword:
|
descent |
| Keyword:
|
crossed modules |
| Keyword:
|
Clifford algebras |
| MSC:
|
16D90 |
| MSC:
|
18N10 |
| MSC:
|
53C27 |
| MSC:
|
55R65 |
| idZBL:
|
Zbl 08141783 |
| idMR:
|
MR4918785 |
| DOI:
|
10.21136/HS.2025.02 |
| . |
| Date available:
|
2026-03-13T14:14:51Z |
| Last updated:
|
2026-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153483 |
| . |
| Reference:
|
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