Deletion-restriction for sheaf homology of graded atomic lattices
arXiv:1902.00399 · doi:10.1016/j.aim.2022.108354
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.