44 citations · 143 across the 17 of their papers we have counts for
22 papers
On the signature of a positive braid
Joshua Evan Greene, Livio Liechti
We show that the signature of a positive braid link is bounded from below by one-quarter of its first Betti number. This equates to one-half of the optimal bound conjectured by Fel…
Alternating links, rational balls, and cube tilings
Joshua Evan Greene, Brendan Owens
When does the double cover of the three-sphere branched along an alternating link bound a rational homology ball? Heegaard Floer homology generates a necessary condition for it to…
Fibered simple knots
Joshua Evan Greene, John Luecke
We prove that a simple knot in the lens space fibers if and only if its order in homology does not divide any remainder occurring in the Euclidean algorithm applied to the…
Cyclic quadrilaterals and smooth Jordan curves
Joshua Evan Greene, Andrew Lobb
For every smooth Jordan curve and cyclic quadrilateral in the Euclidean plane, we show that there exists an orientation-preserving similarity taking the vertices of to…
The Rectangular Peg Problem
Joshua Evan Greene, Andrew Lobb
For every smooth Jordan curve and rectangle in the Euclidean plane, we show that there exists a rectangle similar to whose vertices lie on . The proof relies on Shev…
On curves intersecting at most once, II
Joshua Evan Greene
We prove that on a closed, orientable surface of genus , a set of simple loops with the property that no two are homotopic or intersect in more than points has cardinality $…