Stein-fillability and positivity in the mapping class group
arXiv:2405.07707
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.
v2: 7 pages, 2 figures; to appear in the Journal of Symplectic Geometry; v1: 6 pages, 2 figures. Comments are welcome!