Positivity of Intersections and Tameness of Almost Complex 4-manifolds

2024/01/30 by Cattalani, Spencer
#32Q60 #32Q65 #53C15 #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2401.17381

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.

Related

• Intersection of almost complex submanifolds
• Embedded surfaces and almost complex structures
• Positivity of Boundary Intersections of Complex Curves and Adjunction Formula
• Pseudoholomorphic curves in four-orbifolds and some applications
• The curve cone of almost complex 4-manifolds