99 citations · 649 across the 34 of their papers we have counts for
34 papers
Grope metrics on the knot concordance set
Tim D. Cochran, Shelly Harvey, Mark Powell
To a special type of grope embedded in 4-space, that we call an admissible grope, we associate a length function for each real number q at least 1. This gives rise to a family of p…
Cut open null-bordisms and derivatives of slice knots
Tim Cochran, Christopher William Davis
In the 60's Levine proved that if is a slice knot, then on any genus Seifert surface for there is a component link , called a derivative of , on which the Sei…
Shake slice and shake concordant knots
Tim D. Cochran, Arunima Ray
A crucial step in the surgery-theoretic program to classify smooth manifolds is that of representing a middle--dimensional homology class by a smoothly embedded sphere. This step f…
The geometry of the knot concordance space
Tim D. Cochran, Shelly Harvey
Most of the 50-year history of the study of the set of knot concordance classes, C, has focused on its structure as an abelian group. Here we take a different approach, namely we s…
Positive Links
Tim D. Cochran, Eamonn Tweedy
Given a link L in the 3-sphere, we ask whether the components of L bound disjoint, nullhomologous disks properly embedded in a simply-connected positive-definite smooth 4-manifold;…
Counterexamples to Kauffman's Conjectures on Slice Knots
Tim D. Cochran, Christopher William Davis
In 1982 Louis Kauffman conjectured that if a knot in the 3-sphere is a slice knot then on any Seifert surface for that knot there exists a homologically essential simple closed cur…