The spinor bundle on loop space
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914818085093376 |
|---|---|
| author | Ludewig, Matthias |
| author_facet | Ludewig, Matthias |
| contents | We give a construction of the spinor bundle of the loop space of a string manifold together with its fusion product, inspired by ideas from Stolz and Teichner. The spinor bundle is a super bimodule bundle for a bundle of Clifford von Neumann algebras over the free path space, and the fusion product is defined using Connes fusion of such bimodules. As the main result, we prove that a spinor bundle with fusion product on a manifold X exists if and only X admits a string structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_12521 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The spinor bundle on loop space Ludewig, Matthias Differential Geometry Algebraic Topology Operator Algebras We give a construction of the spinor bundle of the loop space of a string manifold together with its fusion product, inspired by ideas from Stolz and Teichner. The spinor bundle is a super bimodule bundle for a bundle of Clifford von Neumann algebras over the free path space, and the fusion product is defined using Connes fusion of such bimodules. As the main result, we prove that a spinor bundle with fusion product on a manifold X exists if and only X admits a string structure. |
| title | The spinor bundle on loop space |
| topic | Differential Geometry Algebraic Topology Operator Algebras |
| url | https://arxiv.org/abs/2305.12521 |