15 citations · 64 across the 24 of their papers we have counts for
26 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…
Tangle contact homology
Johan Asplund
Knot contact homology is an ambient isotopy invariant of knots and links in . The purpose of this paper is to extend this definition to an ambient isotopy invariant of…
Simplicial descent for Chekanov-Eliashberg dg-algebras
Johan Asplund
We introduce a type of surgery decomposition of Weinstein manifolds we call simplicial decompositions. The main result of this paper is that the Chekanov-Eliashberg dg-algebra of t…
Chekanov-Eliashberg dg-algebras for singular Legendrians
Johan Asplund, Tobias Ekholm
The Chekanov-Eliashberg dg-algebra is a holomorphic curve invariant associated to Legendrian submanifolds of a contact manifold. We extend the definition to Legendrian embeddings o…
Fiber Floer cohomology and conormal stops
Johan Asplund
Let be a closed orientable spin manifold. Let be a submanifold and denote its complement by . In this paper we prove that there exists an isomorphism between…