4 citations · 11 across the 11 of their papers we have counts for
11 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…
Exact Lagrangian tori in symplectic Milnor fibers constructed with fillings
Orsola Capovilla-Searle
We use exact Lagrangian fillings and Weinstein handlebody diagrams to construct infinitely many distinct exact Lagrangian tori in -dimensional Milnor fibers of isolated hypersur…
Weinstein handlebodies for complements of smoothed toric divisors
Bahar Acu, Orsola Capovilla-Searle, Agnès Gadbled +4
We study the interactions between toric manifolds and Weinstein handlebodies. We define a partially-centered condition on a Delzant polytope, which we prove ensures that the comple…
Non-Orientable Lagrangian Cobordisms between Legendrian Knots
Orsola Capovilla-Searle, Lisa Traynor
In the symplectization of standard contact -space, , it is known that an orientable Lagrangian cobordism between a Legendrian knot and itself, also…
Multi-crossing Number for Knots and the Kauffman Bracket Polynomial
Colin Adams, Orsola Capovilla-Searle, Jesse Freeman +5
A multi-crossing (or n-crossing) is a singular point in a projection at which n strands cross so that each strand bisects the crossing. We generalize the classic result of Kauffman…
Bounds on Übercrossing and Petal Numbers for Knots
Colin Adams, Orsola Capovilla-Searle, Jesse Freeman +5
An -crossing is a point in the projection of a knot where strands cross so that each strand bisects the crossing. An übercrossing projection has a single -crossing and a…