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

Brent Everitt; Paul Turner

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arXiv · 0808.1686

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

Brent Everitt·Paul Turner

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

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Brent Everitt, Paul Turner. 2010-08-26. Bundles of coloured posets and a Leray-Serre spectral sequence for Khovanov homology. https://arxiv.org/abs/0808.1686

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