Almost positive links are strongly quasipositive

Autor: Peter Feller, Lukas Lewark, Andrew Lobb

Publikováno v: Mathematische annalen, 2023, Vol.385(1-2), pp.481-510 [Peer Reviewed Journal]
Mathematische Annalen, 385 (1)
Feller, Peter; Lewark, Lukas; Lobb, Andrew (2023). Almost positive links are strongly quasipositive. Mathematische Annalen, 385(1-2), pp. 481-510. Springer 10.1007/s00208-021-02328-x

We prove that any link admitting a diagram with a single negative crossing is strongly quasipositive. This answers a question of Stoimenow's in the (strong) positive. As a second main result, we give a simple and complete characterization of link dia

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9ebe620af052b322e69a0264d09a4c95
http://dro.dur.ac.uk/35394/

The rectangular peg problem

Autor: Joshua Evan Greene, Andrew Lobb

Publikováno v: Annals of Mathematics, 2021, Vol.194(2), pp.509-517 [Peer Reviewed Journal]

For every smooth Jordan curve $\gamma$ and rectangle $R$ in the Euclidean plane, we show that there exists a rectangle similar to $R$ whose vertices lie on $\gamma$. The proof relies on Shevchishin's theorem that the Klein bottle does not admit a smo

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::adece6ea478ffea9ba55201e51a7aaf4
https://doi.org/10.4007/annals.2021.194.2.4

Khovanov homotopy calculations using flow category calculus

Autor: Andrew Lobb, Patrick Orson, Dirk Schütz

Publikováno v: Experimental mathematics, 2020, Vol.29(4), pp.475-500 [Peer Reviewed Journal]

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 two Steenrod squares. We develop a new algorithm which implements the f

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::92646f8a16bf3a7da9ea7745e822cf24
http://dro.dur.ac.uk/25161/

Threaded rings that swim in excitable media

Autor: David Evans, Kate E. Horner, Paul Sutcliffe, Brette M. Chapin, Jonathan W. Steed, Fabian Maucher, Elizabeth H. C. Bromley, Antonio Cincotti, Andrew Lobb

Publikováno v: Physical review letters, 2019, Vol.123(25) [Peer Reviewed Journal]
Cincotti, A, Maucher, F M B M J, Evans, D, Chapin, B M, Horner, K, Bromley, E, Lobb, A, Steed, J W & Sutcliffe, P 2019, ' Threaded Rings that Swim in Excitable Media ', Physical Review Letters, vol. 123, no. 25, 258102 . https://doi.org/10.1103/PhysRevLett.123.258102

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. Here we consider a novel topological configuration i

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1febe26c93942d2d89e8b7e87cc553fc
http://arxiv.org/abs/1908.08751

On the functoriality of Khovanov-Floer theories

Autor: Andrew Lobb, John A. Baldwin, Matthew Hedden

Publikováno v: Advances in mathematics, 2019, Vol.345, pp.1162-1205 [Peer Reviewed Journal]

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 naturally isomorphic to the Khovanov homology of t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::50ebda9dea227ba5b8d2340298dd2022
http://dro.dur.ac.uk/27188/