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arXiv · 2401.17381

Positivity of Intersections and Tameness of Almost Complex 4-manifolds

Spencer Cattalani
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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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Spencer Cattalani. 2024-01-30. Positivity of Intersections and Tameness of Almost Complex 4-manifolds. https://doi.org/10.1007/s00029-026-01134-0

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