Augmentations, Fillings, and Clusters
Symplectic Geometry
2024-02-01 v2 Algebraic Geometry
Geometric Topology
Representation Theory
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.
Keywords
Cite
@article{arxiv.2008.10793,
title = {Augmentations, Fillings, and Clusters},
author = {Honghao Gao and Linhui Shen and Daping Weng},
journal= {arXiv preprint arXiv:2008.10793},
year = {2024}
}
Comments
62 pages. The new version combines the previous version and 2009.00499