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A geometric description of the extreme Khovanov cohomology

Published online by Cambridge University Press:  28 December 2017

J. González-Meneses
Affiliation:
Departamento de Álgebra, Facultad de Matemáticas, Instituto de Matemáticas (IMUS), Universidad de Sevilla, Apdo. 1160, 41080 Sevilla, Spain (meneses@us.es)
P. M. G. Manchón
Affiliation:
Departamento de MatemÁtica Aplicada, ETSIDI-Universidad Politécnica de Madrid, Ronda de Valencia 3, 28012 Madrid, Spain (pedro.gmanchon@upm.es)
M. Silvero
Affiliation:
Departamento de Álgebra, Facultad de MatemÁticas, Instituto de MatemÁticas (IMUS), Universidad de Sevilla, Apdo. 1160, 41080 Sevilla, Spain (marithania@us.es)

Abstract

We prove that the potential extreme Khovanov cohomology of a link is the cohomology of the independence simplicial complex of its Lando graph. We also provide a family of knots having as many non-trivial extreme Khovanov cohomology modules as desired, that is, examples of H-thick knots that are as far from being H-thin as desired.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2018 

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