5 citations · 11 across the 5 of their papers we have counts for
6 papers
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…
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…
Constructions of Lagrangian cobordisms
Sarah Blackwell, Noémie Legout, Caitlin Leverson +6
Lagrangian cobordisms between Legendrian knots arise in Symplectic Field Theory and impose an interesting and not well-understood relation on Legendrian knots. There are some known…
Satellite ruling polynomials, DGA representations, and the colored HOMFLY-PT polynomial
Caitlin Leverson, Dan Rutherford
We establish relationships between two classes of invariants of Legendrian knots in : Representation numbers of the Chekanov-Eliashberg DGA and satellite ruling polyn…
Augmentations and Rulings of Legendrian Links in
Caitlin Leverson
Given a Legendrian link in , we extend the definition of a normal ruling from given by Lavrov and Rutherford and show that the existence of an augme…
Augmentations and Rulings of Legendrian Knots
C. Leverson
For any Legendrian knot in (R^3,ker(dz-ydx)), we show that the existence of an augmentation to any field of the Chekanov-Eliashberg differential graded algebra over Z[t,t^{-1}] is…