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.
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