61 citations · 159 across the 7 of their papers we have counts for
7 papers
Transverse string topology and the cord algebra
Somnath Basu, Jason McGibbon, Dennis Sullivan +1
We define a coalgebra structure for open strings transverse to any framed codimension 2 submanifold. When the submanifold is a knot in R^3, we show this structure recovers a specia…
Knot contact homology
Tobias Ekholm, John Etnyre, Lenhard Ng +1
The conormal lift of a link in is a Legendrian submanifold in the unit cotangent bundle of with contact structure equal to the kernel of the Liou…
Filtrations on the knot contact homology of transverse knots
Tobias Ekholm, John Etnyre, Lenhard Ng +1
We construct a new invariant of transverse links in the standard contact structure on R^3. This invariant is a doubly filtered version of the knot contact homology differential gra…
Knots on a positive template have a bounded number of prime factors
Michael C. Sullivan
Templates are branched 2-manifolds with semi-flows used to model `chaotic' hyperbolic invariant sets of flows on 3-manifolds. Knotted orbits on a template correspond to those in th…
Rounding corners of polygons and the embedded contact homology of T^3
Michael Hutchings, Michael C Sullivan
The embedded contact homology (ECH) of a 3-manifold with a contact form is a variant of Eliashberg-Givental-Hofer's symplectic field theory, which counts certain embedded J-holomor…
The periodic Floer homology of a Dehn twist
Michael Hutchings, Michael Sullivan
The periodic Floer homology of a surface symplectomorphism, defined by the first author and M. Thaddeus, is the homology of a chain complex which is generated by certain unions of…
Visually building Smale flows in S3
Michael C Sullivan
A Smale flow is a structurally stable flow with one dimensional invariant sets. We use information from homology and template theory to construct, visualize and in some cases, clas…