Sheaf homology of hyperplane arrangements, Boolean covers and exterior powers
Abstract
We compute the sheaf homology of the intersection lattice of a hyperplane arrangement with coefficients in the graded exterior sheaf of the natural sheaf. This builds on the results of our previous paper, where this homology was computed for the natural sheaf, itself a generalisation of an old result of Lusztig. The computational machinery we develop in this paper is quite different though: sheaf homology is lifted to what we call Boolean covers, where we instead compute homology cellularly. A number of tools are given for the cellular homology of these Boolean covers, including a deletionrestriction long exact sequence.
 Publication:

arXiv eprints
 Pub Date:
 August 2019
 arXiv:
 arXiv:1908.04500
 Bibcode:
 2019arXiv190804500E
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Combinatorics;
 Mathematics  Group Theory