On perturbative invariants of combed three-manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908606231740416 |
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| author | Mandin--Hublé, Yohan |
| author_facet | Mandin--Hublé, Yohan |
| contents | We give a new definition of a universal finite type invariant of three-dimensional oriented rational homology spheres which counts configurations of trivalent graphs in such manifolds. Kontsevich introduced this invariant following Witten's study of the perturbative expansion of the Chern-Simons theory, using parallelizations of three-manifolds. In this article, we use combings instead of parallelizations to get a more flexible and convenient definition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On perturbative invariants of combed three-manifolds Mandin--Hublé, Yohan Geometric Topology 57K16 57K31 55R80 81Q30 We give a new definition of a universal finite type invariant of three-dimensional oriented rational homology spheres which counts configurations of trivalent graphs in such manifolds. Kontsevich introduced this invariant following Witten's study of the perturbative expansion of the Chern-Simons theory, using parallelizations of three-manifolds. In this article, we use combings instead of parallelizations to get a more flexible and convenient definition. |
| title | On perturbative invariants of combed three-manifolds |
| topic | Geometric Topology 57K16 57K31 55R80 81Q30 |
| url | https://arxiv.org/abs/2510.19633 |