16 citations · 37 across the 11 of their papers we have counts for
15 papers
Skein relations for invariants of Legendrian surfaces
Dan Rutherford, Michael G. Sullivan
For Legendrian surfaces in 1-jet spaces, we consider augmentation number invariants that together generalize the ruling polynomial of 1-dimensional Legendrian knots and establish s…
-limits of Legendrians and positive loops
Georgios Dimitroglou Rizell, Michael G. Sullivan
We show that the image of a Legendrian submanifold under a homeomorphism that is the -limit of a sequence of contactomorphisms is again Legendrian, if the image of the submani…
-limits of Legendrian knots and contact non-squeezing
Georgios Dimitroglou Rizell, Michael G. Sullivan
Take a sequence of contactomorphisms of a contact three-manifold that -converges to a homeomorphism. If the images of a Legendrian knot limit to a smooth knot under this seque…
The persistence of a relative Rabinowitz-Floer complex
Georgios Dimitroglou Rizell, Michael G. Sullivan
We give a quantitative refinement of the invariance of the Legendrian contact homology algebra in general contact manifolds. We show that in this general case, the Lagrangian cobor…
Sheaves via augmentations of Legendrian surfaces
Dan Rutherford, Michael G. Sullivan
Given an augmentation for a Legendrian surface in a -jet space, , we explicitly construct an object, , of the (derived) category from arXi…
The persistence of the Chekanov-Eliashberg algebra
Georgios Dimitroglou Rizell, Michael G. Sullivan
We apply the barcodes of persistent homology theory to the Chekanov-Eliashberg algebra of a Legendrian submanifold to deduce displacement energy bounds for arbitrary Legendrians. W…