On uniqueness of symplectic fillings of links of some surface singularities

Olga Plamenevskaya

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arXiv · 2202.03994

On uniqueness of symplectic fillings of links of some surface singularities

Olga Plamenevskaya

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Abstract

We consider the canonical contact structures on links of rational surface singularities with reduced fundamental cycle. These singularities can be characterized by their dual resolution graphs: the graph is a tree, and the weight of each vertex is no greater than its negative valency. In a joint work with Starkston, we previously showed that if the weight of each vertex in the graph is at most -5, the contact structure has a unique symplectic filling (up to symplectic deformation and blow-up). The proof was based on a symplectic analog of de Jong-van Straten's description of smoothings of these singularities. In this paper, we give a short self-contained proof of uniqueness of fillings, via analysis of positive monodromy factorizations for planar open books supporting these contact structures.

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Olga Plamenevskaya. 2022-02-08. On uniqueness of symplectic fillings of links of some surface singularities. https://arxiv.org/abs/2202.03994

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