1 citations · 2 across the 8 of their papers we have counts for
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Vanishing of higher Legendrian homology for rainbow closures
Roger Casals, Alexander Simons
We show that the higher Legendrian homology of any Legendrian link given by the rainbow closure of a positive braid must necessarily vanish. The result is proven in the most genera…
A Lagrangian filling for every cluster seed
Roger Casals, Honghao Gao
We show that each cluster seed in the augmentation variety is inhabited by an embedded exact Lagrangian filling. This resolves the matter of surjectivity of the map from Lagrangian…
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…
Conjugate Fillings and Legendrian Weaves
Roger Casals, Wenyuan Li
First, we show that conjugate Lagrangian fillings, associated to plabic graphs, and Lagrangian fillings obtained as Reeb pinching sequences are both Hamiltonian isotopic to Lagrang…
Lagrangian Skeleta and Plane Curve Singularities
Roger Casals
We construct closed arboreal Lagrangian skeleta associated to links of isolated plane curve singularities. This yields closed arboreal Lagrangian skeleta for Weinstein pairs and We…
Non-simplicity of isocontact embeddings in all higher dimensions
Roger Casals, John B. Etnyre
In this article we show that in any dimension there exist infinitely many pairs of formally contact isotopic isocontact embeddings into the standard contact sphere which are not co…