Stein-fillability and positivity in the mapping class group

Vitalijs Brejevs; Andy Wand

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arXiv · 2405.07707

Stein-fillability and positivity in the mapping class group

Vitalijs Brejevs·Andy Wand

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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.

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Vitalijs Brejevs, Andy Wand. 2024-05-13. Stein-fillability and positivity in the mapping class group. https://arxiv.org/abs/2405.07707

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