44 citations · 46 across the 5 of their papers we have counts for
6 papers
Jordan curves inscribe a positive measure of rectangles
Joshua Evan Greene, Andrew Lobb
Suppose that is a Jordan curve of diameter which encloses a region of area . We prove that there exists a subset of measure at least…
Polynomial Inscriptions
Joshua Evan Greene, Andrew Lobb
We prove that for every smooth Jordan curve and for every set of six concyclic points, there exists a non-constant quadratic polynomial…
Square pegs between two graphs
Joshua Evan Greene, Andrew Lobb
We show that there always exists an inscribed square in a Jordan curve given as the union of two graphs of functions of Lipschitz constant less than . We are motivate…
Floer homology and square pegs
Joshua Evan Greene, Andrew Lobb
We construct a version of Lagrangian Floer homology whose chain complex is generated by the inscriptions of a rectangle into a real analytic Jordan curve. By using its associated s…
Special Alternating Knots are Band Prime
Joe Boninger, Joshua Evan Greene
We prove that a special alternating knot does not decompose as a non-trivial band sum. This restricts concordances from special alternating knots, and we conjecture that special al…
A spanning tree model for the Heegaard Floer homology of a branched double-cover
Joshua Greene
Given a diagram of a link K in S^3, we write down a Heegaard diagram for the branched-double cover Sigma(K). The generators of the associated Heegaard Floer chain complex correspon…