Stein-fillability and positivity in the mapping class group
Geometric Topology
2025-07-10 v2 Symplectic Geometry
Abstract
We construct an infinite family of non-positive open books with once-punctured torus pages that support Stein-fillable contact structures. Combined with a result of Wendl, this allows us to give a complete answer to a long-standing question about the mapping class group of a compact surface with boundary: namely, we conclude that the monoid of monodromies supporting Stein-fillable contact structures is equal to the monoid of positive monodromies if and only if the surface is planar.
Keywords
Cite
@article{arxiv.2405.07707,
title = {Stein-fillability and positivity in the mapping class group},
author = {Vitalijs Brejevs and Andy Wand},
journal= {arXiv preprint arXiv:2405.07707},
year = {2025}
}
Comments
v2: 7 pages, 2 figures; to appear in the Journal of Symplectic Geometry; v1: 6 pages, 2 figures. Comments are welcome!