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On the functoriality of Khovanov-Floer theories
We introduce the notion of a Khovanov-Floer theory. Roughly, such a theory assigns a filtered chain complex over Z/2 to a link diagram such that (1) the E_2 page of the resulting spectral sequence is… Expand
Computable bounds for Rasmussen’s concordance invariant
- Andrew Lobb
- Compositio Mathematica
- 19 August 2009
Abstract Given a diagram D of a knot K, we give easily computable bounds for Rasmussen’s concordance invariant s(K). The bounds are not independent of the diagram D chosen, but we show that for… Expand
A note on Gornik's perturbation of Khovanov-Rozansky homology.
- Andrew Lobb
- 13 December 2010
We show that the information contained in the associated graded vector space to Gornik’s version of Khovanov‐Rozansky knot homology is equivalent to a single even integer sn.K/. Furthermore we show… Expand
2-strand twisting and knots with identical quantum knot homologies
- Andrew Lobb
- 8 March 2011
Given a knot, we ask how its Khovanov and Khovanov‐Rozansky homologies change under the operation of introducing twists in a pair of strands. We obtain long exact sequences in homology and further… Expand
The quantum sl(n) graph invariant and a moduli space
We associate a moduli problem to a colored trivalent graph; such graphs, when planar, appear in the state-sum description of the quantum sl(N) knot polynomial due to Murakami, Ohtsuki, and Yamada. We… Expand
New Quantum Obstructions to Sliceness
It is well-known that generic perturbations of the complex Frobenius algebra used to define Khovanov cohomology each give rise to Rasmussen's concordance invariant s. This gives a concordance… Expand
Threaded Rings that Swim in Excitable Media.
- A. Cincotti, F. Maucher, +6 authors P. Sutcliffe
- Physics, Medicine
- Physical review letters
- 23 August 2019
Cardiac tissue and the Belousov-Zhabotinsky reaction provide two notable examples of excitable media that support scroll waves, in which a filament core is the source of spiral waves of excitation.… Expand
An sl_n stable homotopy type for matched diagrams
There exists a simplified Bar-Natan Khovanov complex for open 2-braids. The Khovanov cohomology of a knot diagram made by gluing tangles of this type is therefore often amenable to calculation. We… Expand
Framed cobordism and flow category moves.
Framed flow categories were introduced by Cohen, Jones and Segal as a way of encoding the flow data associated to a Floer functional. A framed flow category gives rise to a CW complex with one cell… Expand