Article ID Journal Published Year Pages File Type
4584313 Journal of Algebra 2015 43 Pages PDF
Abstract

We define several homology theories for central hyperplane arrangements, categorifying well-known polynomial invariants including the characteristic polynomial, Poincaré polynomial, and Tutte polynomial. We consider basic algebraic properties of such chain complexes, including long-exact sequences associated to deletion–restriction triples and dg-algebra structures. We also consider signed hyperplane arrangements, and generalize the odd Khovanov homology of Ozsváth–Rasmussen–Szabó from link projections to signed arrangements. We define hyperplane Reidemeister moves which generalize the usual Reidemeister moves from framed link projections to signed arrangements, and prove that the chain homotopy type associated to a signed arrangement is invariant under hyperplane Reidemeister moves.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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