New geometric structures on 3-manifolds: surgery and generalized geometry
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913177106644992 |
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| author | Porti, Joan Rubio, Roberto |
| author_facet | Porti, Joan Rubio, Roberto |
| contents | Cosymplectic and normal almost contact structures are analogues of symplectic and complex structures that can be defined on 3-manifolds. Their existence imposes strong topological constraints. Generalized geometry offers a natural common generalization of these two structures: $B_3$-generalized complex structures. We prove that any closed orientable 3-manifold admits such a structure, which can be chosen to be stable, that is, generically cosymplectic up to generalized diffeomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_12471 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New geometric structures on 3-manifolds: surgery and generalized geometry Porti, Joan Rubio, Roberto Differential Geometry Geometric Topology Symplectic Geometry Cosymplectic and normal almost contact structures are analogues of symplectic and complex structures that can be defined on 3-manifolds. Their existence imposes strong topological constraints. Generalized geometry offers a natural common generalization of these two structures: $B_3$-generalized complex structures. We prove that any closed orientable 3-manifold admits such a structure, which can be chosen to be stable, that is, generically cosymplectic up to generalized diffeomorphism. |
| title | New geometric structures on 3-manifolds: surgery and generalized geometry |
| topic | Differential Geometry Geometric Topology Symplectic Geometry |
| url | https://arxiv.org/abs/2402.12471 |