The stringor bundle
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909178510966784 |
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| author | Kristel, Peter Ludewig, Matthias Waldorf, Konrad |
| author_facet | Kristel, Peter Ludewig, Matthias Waldorf, Konrad |
| contents | We set up a framework of 2-Hilbert bundles, which allows to rigorously define the "stringor bundle", a higher differential geometric object anticipated by Stolz and Teichner in an unpublished preprint about 20 years ago. Our framework includes an associated bundle construction, allowing us to associate a 2-Hilbert bundle with a principal 2-bundle and a unitary representation of its structure 2-group. We prove that the Stolz-Teichner stringor bundle is canonically isomorphic to the 2-Hilbert bundle obtained from applying our associated bundle construction to a string structure on a manifold and the stringor representation of the string 2-group that we discovered in earlier work. This establishes a perfect analogy to spin manifolds, representations of the spin groups, and spinor bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_09797 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The stringor bundle Kristel, Peter Ludewig, Matthias Waldorf, Konrad Algebraic Topology Mathematical Physics Differential Geometry Operator Algebras We set up a framework of 2-Hilbert bundles, which allows to rigorously define the "stringor bundle", a higher differential geometric object anticipated by Stolz and Teichner in an unpublished preprint about 20 years ago. Our framework includes an associated bundle construction, allowing us to associate a 2-Hilbert bundle with a principal 2-bundle and a unitary representation of its structure 2-group. We prove that the Stolz-Teichner stringor bundle is canonically isomorphic to the 2-Hilbert bundle obtained from applying our associated bundle construction to a string structure on a manifold and the stringor representation of the string 2-group that we discovered in earlier work. This establishes a perfect analogy to spin manifolds, representations of the spin groups, and spinor bundles. |
| title | The stringor bundle |
| topic | Algebraic Topology Mathematical Physics Differential Geometry Operator Algebras |
| url | https://arxiv.org/abs/2206.09797 |