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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Bundles of coloured posets and a Leray-Serre spectral sequence for Khovanov homology


Authors: Brent Everitt and Paul Turner
Journal: Trans. Amer. Math. Soc. 364 (2012), 3137-3158
MSC (2010): Primary 57M27; Secondary 06A11, 55T10
Published electronically: January 31, 2012
MathSciNet review: 2888240
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Abstract: The decorated hypercube found in the construction of Khovanov homology for links is an example of a Boolean lattice equipped with a presheaf of modules. One can place this in a wider setting as an example of a coloured poset, that is to say, a poset with a unique maximal element equipped with a presheaf of modules. In this paper we initiate the study of a bundle theory for coloured posets, producing for a certain class of base posets a Leray-Serre type spectral sequence. We then show how this theory finds an application in Khovanov homology by producing a new spectral sequence converging to the Khovanov homology of a given link.


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Additional Information

Brent Everitt
Affiliation: Department of Mathematics, University of York, York YO10 5DD, England
Email: brent.everitt@york.ac.uk

Paul Turner
Affiliation: Département de mathématiques, Université de Fribourg, CH-1700 Fribourg, Switzerland – and – Section de mathématiques, Université de Genève, 2-4 rue du Lièvre, CH-1211, Geneva, Switzerland
Email: prt.maths@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05459-6
Keywords: Coloured poset, spectral sequence, poset bundle, Khovanov homology
Received by editor(s): January 16, 2009
Received by editor(s) in revised form: August 25, 2010
Published electronically: January 31, 2012
Additional Notes: The first author thanks Finnur Larusson for many useful and stimulating discussions. He is also grateful to the Alpine Mathematical Institute, Haute-Savoie, France, and to the Institute for Geometry and its Applications, University of Adelaide, Australia.
The second author was partially supported by the Swiss National Science Foundation projects no. 200020-113199 and no. 200020-121506.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.