Equivariant cohomological rigidity for four-dimensional Hamiltonian $\mathbf{S^1}$-manifolds
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913618249908224 |
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| author | Holm, Tara S. Kessler, Liat Tolman, Susan |
| author_facet | Holm, Tara S. Kessler, Liat Tolman, Susan |
| contents | For manifolds equipped with group actions, we have the following natural question: To what extent does the equivariant cohomology determine the equivariant diffeotype? We resolve this question for Hamiltonian circle actions on compact, connected symplectic four-manifolds. They are equivariantly diffeomorphic if and only if their equivariant cohomology rings are isomorphic as algebras over the equivariant cohomology of a point. In fact, we prove a stronger claim: each isomorphism between their equivariant cohomology rings is induced by an equivariant diffeomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_14310 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant cohomological rigidity for four-dimensional Hamiltonian $\mathbf{S^1}$-manifolds Holm, Tara S. Kessler, Liat Tolman, Susan Symplectic Geometry Differential Geometry 53D35 (55N91, 53D20, 57S15) For manifolds equipped with group actions, we have the following natural question: To what extent does the equivariant cohomology determine the equivariant diffeotype? We resolve this question for Hamiltonian circle actions on compact, connected symplectic four-manifolds. They are equivariantly diffeomorphic if and only if their equivariant cohomology rings are isomorphic as algebras over the equivariant cohomology of a point. In fact, we prove a stronger claim: each isomorphism between their equivariant cohomology rings is induced by an equivariant diffeomorphism. |
| title | Equivariant cohomological rigidity for four-dimensional Hamiltonian $\mathbf{S^1}$-manifolds |
| topic | Symplectic Geometry Differential Geometry 53D35 (55N91, 53D20, 57S15) |
| url | https://arxiv.org/abs/2412.14310 |