Positivity of Intersections and Tameness of Almost Complex 4-manifolds
arXiv:2401.17381 · doi:10.1007/s00029-026-01134-0
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.
25 pages, 1 figure; improved clarity, especially in Section 5; published in Selecta Mathematica