Deletion-restriction for sheaf homology of graded atomic lattices

Brent Everitt; Paul Turner

Deletion-restriction for sheaf homology of graded atomic lattices

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arxiv 1902.00399 v2 pith:IXYZZU5F submitted 2019-02-01 math.AT math.COmath.GR

Brent Everitt , Paul Turner This is my paper · ORCID

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keywords homologysheafarrangementatomicequippedgradedlatticelattices

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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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Sheaf homology of hyperplane arrangements, Boolean covers and exterior powers
math.AT 2019-08 conditional novelty 6.0 of 10

For an essential hyperplane arrangement, the sheaf homology of its intersection lattice with coefficients in the exterior powers of the natural sheaf is concentrated on one diagonal, with dimensions given by derivativ...

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