J. Hughes

collaborators

5 papers

math.SG2026

Exact Lagrangian fillability of 3-braid closures

James Hughes, Jiajie Ma

We determine when a Legendrian quasipositive 3-braid closure in standard contact $R^{3}$ admits an orientable or non-orientable exact Lagrangian filling. Our main result pro…

math.SG2025

Exact Lagrangian fillings of twist-spun torus links

Vincent Chen, Patton Galloway, James Hughes +1

We construct exact Lagrangian fillings of Legendrian torus links $I^ (k, n - k)$ that are fixed by a Legendrian loop that acts by $2 I ¨ ℓ / n$ rotation. Using these rotationally symmet…

math.SG2025

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…

math.SG2025

Legendrian doubles, twist spuns, and clusters

James Hughes, Agniva Roy

Let $I^»$ be a Legendrian link in standard contact $R^{3}$ , such that $L_{1}$ , $L_{2}$ are two exact fillings of $I^»$ and $I ¨ $ is a Legendrian loop of $I^»$ . We study fillability…

math.SG2025

Augmentations, Fillings, and Clusters for 2-Bridge Links

Orsola Capovilla-Searle, James Hughes, Daping Weng

We produce the first examples relating non-orientable exact Lagrangian fillings of Legendrian links to cluster theory, showing that the ungraded augmentation variety of certain max…