37 citations · 98 across the 13 of their papers we have counts for
15 papers
Cluster structures from Legendrian double twist knots: a comparative approach
James Hughes, Jiajie Ma
We undertake a systematic comparison of cluster algebras associated to Legendrian knots of the same smooth knot type. We describe a cluster structure on the m-graded augmentation v…
Exact Lagrangian fillings of twist-spun torus links
Vincent Chen, Patton Galloway, James Hughes +1
We construct exact Lagrangian fillings of Legendrian torus links that are fixed by a Legendrian loop that acts by rotation. Using these rotationally symmetri…
Decompositions of augmentation varieties via weaves and rulings
Johan Asplund, Orsola Capovilla-Searle, James Hughes +3
The braid variety of a positive braid and the augmentation variety of a Legendrian link both admit decompositions coming from weaves and rulings, respectively. We prove that these…
Exact Lagrangian fillability of 3-braid closures
James Hughes, Jiajie Ma
We determine when a Legendrian quasipositive 3-braid closure in standard contact admits an orientable or non-orientable exact Lagrangian filling. Our main result pro…
Legendrian doubles, twist spuns, and clusters
James Hughes, Agniva Roy
Let be a Legendrian link in standard contact , such that , are two exact fillings of and is a Legendrian loop of . We study fillability and…
Legendrian loops and cluster modular groups
James Hughes
This work studies Legendrian loop actions on exact Lagrangian fillings of Legendrian links in $(\R^3, ξ_{\st})$. By identifying the induced action of Legendrian loops as generators…