4 citations · 4 across the 7 of their papers we have counts for
8 papers
On Ruling polynomials of Legendrian links
Orsola Capovilla-Searle, Yu Pan
The ruling polynomial is a Legendrian invariant that is closely related to the augmentation variety of the Legendrian. We characterize all graded and ungraded ruling polynomials, a…
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…
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…
On Newton polytopes of Lagrangian augmentations
Orsola Capovilla-Searle, Roger Casals
This note explores the use of Newton polytopes in the study of Lagrangian fillings of Legendrian submanifolds. In particular, we show that Newton polytopes associated to augmented…
Lagrangian cobordism of positroid links
Johan Asplund, Youngjin Bae, Orsola Capovilla-Searle +3
Casals-Gorsky-Gorsky-Simental realized all positroid strata of the complex Grassmannian as augmentation varieties of Legendrians called positroid links. We prove that the partial o…
Obstructions to reversing Lagrangian surgery in Lagrangian fillings
Orsola Capovilla-Searle, Noémie Legout, Maÿlis Limouzineau +3
Given an immersed, Maslov-, exact Lagrangian filling of a Legendrian knot, if the filling has a vanishing index and action double point, then through Lagrangian surgery it is po…