Cellular cohomology of posets with local coefficients

We describe a “cellular” approach to the computation of the cohomology of a poset with coefficients in a presheaf. A cellular cochain complex is constructed, described explicitly, and shown to compute the cohomology under certain circumstances. The descriptions are refined further for certain classe...

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Bibliographic Details
Published in:	Journal of algebra Vol. 439; pp. 134 - 158
Main Authors:	Everitt, Brent, Turner, Paul
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01-10-2015
Subjects:	Bruhat order Cellular cohomology Cohomology of a poset with coefficients in a presheaf Geometric lattices Khovanov homology Geometric lattices Cellular cohomology Khovanov homology Cohomology of a poset with coefficients in a presheaf Bruhat order
Online Access:	Get full text
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Summary:	We describe a “cellular” approach to the computation of the cohomology of a poset with coefficients in a presheaf. A cellular cochain complex is constructed, described explicitly, and shown to compute the cohomology under certain circumstances. The descriptions are refined further for certain classes of posets including the cell posets of regular CW-complexes and geometric lattices.
ISSN:	0021-8693 1090-266X
DOI:	10.1016/j.jalgebra.2015.05.007