6 citations · 13 across the 5 of their papers we have counts for
7 papers · 1 filter
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…
A counterexample to Batson's conjecture
Andrew Lobb
We show that the torus knot bounds a smooth Möbius band in the -ball, giving a counterexample to Batson's non-orientable analogue of Milnor's conjecture on the smooth…
Khovanov homotopy calculations using flow category calculus
Andrew Lobb, Patrick Orson, Dirk Schuetz
The Lipshitz-Sarkar stable homotopy link invariant defines Steenrod squares on the Khovanov cohomology of a link. Lipshitz-Sarkar constructed an algorithm for computing the first t…
The Dold-Whitney theorem and the Sato-Levine invariant
Andrew Lobb
We use the Dold-Whitney theorem classifying -bundles over a 4-complex to give a mod 4 obstruction to a 2-component link of trivial linking number being slice. It turns out t…
Morse moves in flow categories
Dan Jones, Andrew Lobb, Dirk Schuetz
We pursue the analogy of a framed flow category with the flow data of a Morse function. In classical Morse theory, Morse functions can sometimes be locally altered and simplified b…