Planar contact 3-manifolds with infinitely many Stein fillings

R. Inanc Baykur

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arXiv · 2607.21303

Planar contact 3-manifolds with infinitely many Stein fillings

R. Inanc Baykur

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Abstract

We prove that there are infinitely many closed contact 3-manifolds supported by planar open books, each admitting infinitely many pairwise non-homeomorphic Stein fillings. This answers K3 Problem 4.105. As a corollary, there are contact 3-manifolds that admit infinitely many Stein fillings but do not admit arbitrarily large ones.

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R. Inanc Baykur. 2026-07-23. Planar contact 3-manifolds with infinitely many Stein fillings. https://arxiv.org/abs/2607.21303

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