Stein-fillability and positivity in the mapping class group
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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Advanced Operator Algebra Research
Holomorphic and Operator Theory
Publication details
- Journal / source
- Journal of Symplectic Geometry
- Volume
- 24
- Issue
- 2
- Pages
- 467–477
- Publication date
- 1 January 2026
- Language
- EN