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Deletion-restriction for sheaf homology of graded atomic lattices

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JournalAdvances in Mathematics
DateAccepted/In press - 10 Mar 2022
DateE-pub ahead of print - 25 Mar 2022
DatePublished (current) - 25 Jun 2022
Volume402
Number of pages24
Early online date25/03/22
Original languageEnglish

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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© 2022 Elsevier Inc. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy.

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