Mathematics – Geometric Topology
Scientific paper
2008-08-12
Trans. Amer. Math. Soc., 364 (6), 2012, 3137-3158
Mathematics
Geometric Topology
22 pages; minor changes since version 1, including the addition of the words, "for Khovanov homology" to the end of the title
Scientific paper
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.
Everitt Brent
Turner Paul
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