Deletion-restriction for sheaf homology of graded atomic lattices

Brent Everitt; Paul Turner

doi:10.1016/j.aim.2022.108354

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arXiv · 1902.00399

Deletion-restriction for sheaf homology of graded atomic lattices

Brent Everitt·Paul Turner

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Abstract

We give a long exact sequence for the homology of a graded atomic lattice equipped with a sheaf of modules, in terms of the deleted and restricted lattices. This is then used to compute the homology of the arrangement lattice of a hyperplane arrangement equipped with the natural sheaf. This generalises an old result of Lusztig.

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Brent Everitt, Paul Turner. 2019-02-01. Deletion-restriction for sheaf homology of graded atomic lattices. https://doi.org/10.1016/j.aim.2022.108354

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