Odd Khovanov homology for hyperplane arrangements

Zsuzsanna Dancso*, Anthony Licata

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)102-144
    Number of pages43
    JournalJournal of Algebra
    Publication statusPublished - 5 Aug 2015


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