Cellular cohomology of posets with local coefficients
Brent Everitt, Paul Turner
TL;DR
This paper introduces a cellular method for computing the cohomology of posets with local coefficients, providing explicit complexes and refinements for specific classes like CW-complexes and lattices.
Contribution
It develops a cellular cochain complex framework for poset cohomology with local coefficients, enhancing computational techniques and applicability.
Findings
Constructed explicit cellular cochain complexes
Proved the complexes compute cohomology under certain conditions
Refined descriptions for regular CW-complexes and geometric lattices
Abstract
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.
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