Boundary framings for locally conformally symplectic four-manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912352260063232 |
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| author | Morava, J |
| author_facet | Morava, J |
| contents | We construct a rational homotopy-theoretic model for a classifying space of locally conformally symplectic structures on four-manifolds, and use it to definition a cobordism category of three-manifolds `anchored' by principal $Ω^2 S^2$ - bundles ($\S2$, generalizing contact structures). Powerful $sl_2$ - representation-valued Hodge-Lefschetz cohomology (going back to Chern and Weil), taking values in the $\mathbb{Z}$-graded category of bidifferential modules of Angella, Otiman, and Tardini is available for its study.
This is an extended revision with a detailed introduction replacing the final section. The original concern of the paper was a characteristic two issue which remains unchanged. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_05983 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary framings for locally conformally symplectic four-manifolds Morava, J Algebraic Topology 57R56, 11M32 We construct a rational homotopy-theoretic model for a classifying space of locally conformally symplectic structures on four-manifolds, and use it to definition a cobordism category of three-manifolds `anchored' by principal $Ω^2 S^2$ - bundles ($\S2$, generalizing contact structures). Powerful $sl_2$ - representation-valued Hodge-Lefschetz cohomology (going back to Chern and Weil), taking values in the $\mathbb{Z}$-graded category of bidifferential modules of Angella, Otiman, and Tardini is available for its study. This is an extended revision with a detailed introduction replacing the final section. The original concern of the paper was a characteristic two issue which remains unchanged. |
| title | Boundary framings for locally conformally symplectic four-manifolds |
| topic | Algebraic Topology 57R56, 11M32 |
| url | https://arxiv.org/abs/2502.05983 |