Mathematics > Symplectic Geometry
[Submitted on 25 Aug 2020 (v1), last revised 31 Jan 2024 (this version, v2)]
Title:Augmentations, Fillings, and Clusters
View PDF HTML (experimental)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.
Submission history
From: Honghao Gao [view email][v1] Tue, 25 Aug 2020 03:10:01 UTC (87 KB)
[v2] Wed, 31 Jan 2024 03:51:04 UTC (92 KB)
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