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arXiv · 2008.10793

Augmentations, Fillings, and Clusters

Honghao Gao·Linhui Shen·Daping Weng
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Abstract

We investigate positive braid Legendrian links via a Floer-theoretic approach and prove that their augmentation varieties are cluster K2 (aka. A-) varieties. Using the exact Lagrangian cobordisms of Legendrian links in [EHK16], we prove that a large family of exact Lagrangian fillings of positive braid Legendrian links correspond to cluster seeds of their augmentation varieties. We solve the infinite-filling problem for positive braid Legendrian links; i.e., whenever a positive braid Legendrian link is not of type ADE, it admits infinitely many exact Lagrangian fillings up to Hamiltonian isotopy.

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Honghao Gao, Linhui Shen, Daping Weng. 2020-08-25. Augmentations, Fillings, and Clusters. https://arxiv.org/abs/2008.10793

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