The Clifford Algebra Bundle on Loop Space
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 tran...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2024 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212103 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Clifford Algebra Bundle on Loop Space. Matthias Ludewig. SIGMA 20 (2024), 020, 27 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862647538765529088 |
|---|---|
| author | Ludewig, Matthias |
| author_facet | Ludewig, Matthias |
| citation_txt | The Clifford Algebra Bundle on Loop Space. Matthias Ludewig. SIGMA 20 (2024), 020, 27 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2026-03-15T12:32:10Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212103 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-15T12:32:10Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ludewig, Matthias 2026-01-28T13:54:54Z 2024 The Clifford Algebra Bundle on Loop Space. Matthias Ludewig. SIGMA 20 (2024), 020, 27 pages 1815-0659 2020 Mathematics Subject Classification: 15A66; 53C27; 46L40 arXiv:2204.00798 https://nasplib.isofts.kiev.ua/handle/123456789/212103 https://doi.org/10.3842/SIGMA.2024.020 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. It is a pleasure to thank Achim Krause, David Roberts, Raphael Schmidpeter, and Konrad Waldorf for helpful discussions. I would also thank the anonymous referees for their suggestions, which improved the paper. I am indebted to SFB 1085 “Higher Invariants” for financial support. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Clifford Algebra Bundle on Loop Space Article published earlier |
| spellingShingle | The Clifford Algebra Bundle on Loop Space Ludewig, Matthias |
| title | The Clifford Algebra Bundle on Loop Space |
| title_full | The Clifford Algebra Bundle on Loop Space |
| title_fullStr | The Clifford Algebra Bundle on Loop Space |
| title_full_unstemmed | The Clifford Algebra Bundle on Loop Space |
| title_short | The Clifford Algebra Bundle on Loop Space |
| title_sort | clifford algebra bundle on loop space |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212103 |
| work_keys_str_mv | AT ludewigmatthias thecliffordalgebrabundleonloopspace AT ludewigmatthias cliffordalgebrabundleonloopspace |