English

Symplectic surfaces and bridge position

Geometric Topology 2019-04-11 v1

Abstract

We give a new characterization of symplectic surfaces in CP^2 via bridge trisections. Specifically, a minimal genus surface in CP^2 is smoothly isotopic to a symplectic surface if and only if it is smoothly isotopic to a surface in transverse bridge position. We discuss several potential applications, including the classification of unit 2-knots, establishing the triviality of Gluck twists, the symplectic isotopy problem, Auroux's proof that every symplectic 4-manifold is a branched cover over CP^2, and the existence of Weinstein trisections. The proof exploits a well-known connection between symplectic surfaces and quasipositive factorizations of the full twist in the braid group.

Keywords

Cite

@article{arxiv.1904.05137,
  title  = {Symplectic surfaces and bridge position},
  author = {Peter Lambert-Cole},
  journal= {arXiv preprint arXiv:1904.05137},
  year   = {2019}
}

Comments

13 pages, 3 figures

R2 v1 2026-06-23T08:35:18.404Z