The Clifford Algebra Bundle on Loop Space
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866910362952007680 |
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| author | Ludewig, Matthias |
| author_facet | Ludewig, Matthias |
| contents | We construct a Clifford algebra bundle formed from the tangent bundle of the smooth loop space of a Riemannian manifold, which is a bundle of super von Neumann algebras on the loop space. We show that this bundle is in general non-trivial, more precisely that its triviality is obstructed by the transgressions of the second Stiefel-Whitney class and the first (fractional) Pontrjagin class of the manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_00798 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Clifford Algebra Bundle on Loop Space Ludewig, Matthias Differential Geometry Algebraic Topology Operator Algebras We construct a Clifford algebra bundle formed from the tangent bundle of the smooth loop space of a Riemannian manifold, which is a bundle of super von Neumann algebras on the loop space. We show that this bundle is in general non-trivial, more precisely that its triviality is obstructed by the transgressions of the second Stiefel-Whitney class and the first (fractional) Pontrjagin class of the manifold. |
| title | The Clifford Algebra Bundle on Loop Space |
| topic | Differential Geometry Algebraic Topology Operator Algebras |
| url | https://arxiv.org/abs/2204.00798 |