24 citations · 58 across the 9 of their papers we have counts for
9 papers
A Lagrangian filling for every cluster seed
Roger Casals, Honghao Gao
We show that each cluster seed in the augmentation variety is inhabited by an embedded exact Lagrangian filling. This resolves the matter of surjectivity of the map from Lagrangian…
Augmentations and sheaves for links
Honghao Gao
We study the relation between augmentations and sheaves in the context of framed oriented links. In this set up, we find slightly more sheaves than augmentations. After removing th…
Non-fillable augmentations of twist knots
Honghao Gao, Dan Rutherford
We establish new examples of augmentations of Legendrian twist knots that cannot be induced by orientable Lagrangian fillings. To do so, we use a version of the Seidel-Ekholm-Dimit…
Augmentations, Fillings, and Clusters
Honghao Gao, Linhui Shen, Daping Weng
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 Lagran…
Infinitely many Lagrangian fillings
Roger Casals, Honghao Gao
We prove that all maximal-tb Legendrian torus links (n,m) in the standard contact 3-sphere, except for (2,m),(3,3),(3,4) and (3,5), admit infinitely many Lagrangian fillings in the…
Augmentations and link group representations
Honghao Gao
We construct the augmentation representation. It is a representation of the fundamental group of the link complement associated to an augmentation of the framed cord algebra. This…
Simple Sheaves for Knot Conormals
Honghao Gao
We classify the simple sheaves microsupported along the conormal bundle of a knot. We also establish a correspondence between simple sheaves up to local systems and augmentations,…
Radon Transform for Sheaves
Honghao Gao
We define the Radon transform functor for sheaves and prove that it is an equivalence after suitable microlocal localizations. As a result, the sheaf category associated to a Legen…
Spherical Tiling by 12 Congruent Pentagons
Honghao Gao, Nan Shi, Min Yan
The tilings of the 2-dimensional sphere by congruent triangles have been extensively studied, and the edge-to-edge tilings have been completely classified. However, not much is kno…