Augmentations, Fillings, and Clusters

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 br...

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Bibliographic Details
Published in:arXiv.org 2024-01
Main Authors: Gao, Honghao, Shen, Linhui, Weng, Daping
Format: Article
Language:English
Subjects:
Algorithms
Braiding
Clusters
Online Access:Get full text
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Summary: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.
ISSN:2331-8422