English

Positivity of Intersections and Tameness of Almost Complex 4-manifolds

Symplectic Geometry 2024-02-01 v1 Differential Geometry

Abstract

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.

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Cite

@article{arxiv.2401.17381,
  title  = {Positivity of Intersections and Tameness of Almost Complex 4-manifolds},
  author = {Spencer Cattalani},
  journal= {arXiv preprint arXiv:2401.17381},
  year   = {2024}
}

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19 pages