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

TY - JOUR

T1 - Bundles of coloured posets and a Leray-Serre spectral sequence for Khovanov homology

AU - Everitt, Brent

AU - Turner, Paul

PY - 2012/6

Y1 - 2012/6

N2 - 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 application in Khovanov homology by producing a new spectral sequence converging to the Khovanov homology of a given link.

AB - 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 application in Khovanov homology by producing a new spectral sequence converging to the Khovanov homology of a given link.

KW - Algebra, Pure Mathematics

UR - http://www.scopus.com/inward/record.url?scp=84857661767&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-2012-05459-6

DO - 10.1090/S0002-9947-2012-05459-6

M3 - Article

SN - 0002-9947

VL - 364

SP - 3137

EP - 3158

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 6

ER -