Positivity of Intersections and Tameness of Almost Complex 4-manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913216253132800 |
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| author | Cattalani, Spencer |
| author_facet | Cattalani, Spencer |
| contents | We prove that pseudoholomorphic curves intersect complex 2-cycles positively in almost complex 4-manifolds. This makes possible a general and conceptually simple proof that an almost complex 4-manifold with many curves admits a taming symplectic structure, as envisioned by Gromov. Furthermore, we prove that the positivity of intersections between pseudoholomorphic curves is stable, in a geometric sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17381 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Positivity of Intersections and Tameness of Almost Complex 4-manifolds Cattalani, Spencer Symplectic Geometry Differential Geometry 32Q65, 32Q60, 53C15 We prove that pseudoholomorphic curves intersect complex 2-cycles positively in almost complex 4-manifolds. This makes possible a general and conceptually simple proof that an almost complex 4-manifold with many curves admits a taming symplectic structure, as envisioned by Gromov. Furthermore, we prove that the positivity of intersections between pseudoholomorphic curves is stable, in a geometric sense. |
| title | Positivity of Intersections and Tameness of Almost Complex 4-manifolds |
| topic | Symplectic Geometry Differential Geometry 32Q65, 32Q60, 53C15 |
| url | https://arxiv.org/abs/2401.17381 |