75 citations · 138 across the 8 of their papers we have counts for
8 papers · 1 filter
On knot Floer homology and cabling II
Matthew Hedden
We continue our study of the knot Floer homology invariants of cable knots. For large |n|, we prove that many of the filtered subcomplexes in the knot Floer homology filtration ass…
Does Khovanov homology detect the unknot?
Matthew Hedden, Liam Watson
We determine a wide class of knots, which includes unknotting number one knots, within which Khovanov homology detects the unknot. A corollary is that the Khovanov homology of many…
Khovanov homology of the 2-cable detects the unknot
Matthew Hedden
We prove that the Khovanov homology of the 2-cable detects the unknot. A corollary is that Khovanov's categorification of the 2-colored Jones polynomial detects the unknot.
Some remarks on cabling, contact structures, and complex curves
Matthew Hedden
We determine the relationship between the contact structure induced by a fibered knot, K, in the three-sphere and the contact structures induced by its various cables. Understandin…
On Floer homology and the Berge conjecture on knots admitting lens space surgeries
Matthew Hedden
We complete the first step in a two-part program proposed by Baker, Grigsby, and the author to prove that Berge's construction of knots in the three-sphere which admit lens space s…
Grid Diagrams for Lens Spaces and Combinatorial Knot Floer Homology
Kenneth L. Baker, J. Elisenda Grigsby, Matthew Hedden
Similar to knots in S^3, any knot in a lens space has a grid diagram from which one can combinatorially compute all of its knot Floer homology invariants. We give an explicit descr…