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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 isExpand
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Computable bounds for Rasmussen’s concordance invariant
  • Andrew Lobb
  • Mathematics
  • 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 forExpand
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A note on Gornik's perturbation of Khovanov-Rozansky homology.
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 showExpand
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2-strand twisting and knots with identical quantum knot homologies
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 furtherExpand
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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. WeExpand
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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 concordanceExpand
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Threaded Rings that Swim in Excitable Media.
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
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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. WeExpand
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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 cellExpand
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Unknotting the interactive effects of learning processes on cultural evolutionary dynamics
TLDR
We present a mathematical model that specifies how these variant frequencies are affected by non-linear interactions between copying fidelity, mirroring, handedness and repetition biases. Expand
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