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On the functoriality of Khovanov-Floer theories
- John A. Baldwin, M. Hedden, Andrew Lobb
- Mathematics
- 15 September 2015
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
- 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 for… Expand
A note on Gornik's perturbation of Khovanov-Rozansky homology.
- Andrew Lobb
- Mathematics
- 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
- Mathematics
- 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
- Andrew Lobb, Raphael Zentner
- Mathematics
- 24 April 2012
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
- Lukas Lewark, Andrew Lobb
- Mathematics
- 28 January 2015
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
- D. Jones, Andrew Lobb, D. Schuetz
- Mathematics
- 25 June 2015
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.
- Andrew Lobb, Patrick Orson, D. Schuetz
- Mathematics
- 6 May 2016
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
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