Constructions of symplectic surfaces in symplectic 4-manifolds with transversal intersections
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915200159973376 |
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| author | Muñoz, Vicente Rojo, Juan |
| author_facet | Muñoz, Vicente Rojo, Juan |
| contents | In the breakthrough paper [V. Muñoz, A Smale-Barden manifold admitting K-contact but not Sasakian structure, 2024, 10.4171/JEMS/1496], it is constructed the first example of a simply connected compact 5-manifold (aka.\ Smale-Barden manifold) which admits a K-contact structure but does not carry a Sasakian structure, thus settling the question raised as Open Problem 10.2.1 in n [C. Boyer and K. Galicki, Sasakian Geometry, OUP, 2007]. In this paper we revise, refine and generalize the constructions of symplectic surfaces in a symplectic 4-manifold with transversal intersections. These are needed to produce the ramification locus of Seifert bundles over symplectic 4-orbifolds that serve to produce K-contact 5-manifolds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_12428 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructions of symplectic surfaces in symplectic 4-manifolds with transversal intersections Muñoz, Vicente Rojo, Juan Symplectic Geometry Differential Geometry 53D35, 57R17 In the breakthrough paper [V. Muñoz, A Smale-Barden manifold admitting K-contact but not Sasakian structure, 2024, 10.4171/JEMS/1496], it is constructed the first example of a simply connected compact 5-manifold (aka.\ Smale-Barden manifold) which admits a K-contact structure but does not carry a Sasakian structure, thus settling the question raised as Open Problem 10.2.1 in n [C. Boyer and K. Galicki, Sasakian Geometry, OUP, 2007]. In this paper we revise, refine and generalize the constructions of symplectic surfaces in a symplectic 4-manifold with transversal intersections. These are needed to produce the ramification locus of Seifert bundles over symplectic 4-orbifolds that serve to produce K-contact 5-manifolds. |
| title | Constructions of symplectic surfaces in symplectic 4-manifolds with transversal intersections |
| topic | Symplectic Geometry Differential Geometry 53D35, 57R17 |
| url | https://arxiv.org/abs/2503.12428 |