• Corpus ID: 221293123

Augmentations, Fillings, and Clusters

@article{Gao2020AugmentationsFA,
  title={Augmentations, Fillings, and Clusters},
  author={Honghao Gao and Li-Chien Shen and Daping Weng},
  journal={arXiv: Symplectic Geometry},
  year={2020}
}
We prove that the augmentation variety of any positive braid Legendrian link carries a natural cluster $\mathrm{K}_2$ structure. We present an algorithm to calculate the cluster seeds that correspond to the admissible Lagrangian fillings of the positive braid Legendrian links. Utilizing augmentations and cluster algebras, we develop a new framework to distinguish exact Lagrangian fillings. 
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14 Citations
Highly Influential Citations
2
Background Citations
4
Methods Citations
1

14 Citations

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