A geometric duality for order complexes and hyperplane complements

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Abstract

The top cohomology of the complement of an arrangement of complex hyperplanes is canonically isomorphic to the order homology of the associated intersection lattice. We put this result into a geometric framework by constructing a realization of the order complex of the intersection lattice inside the link of the arrangement. The canonical isomorphism is shown to coincide with the restriction of the classical Alexander duality mapping. Thus the isomorphism is a consequence of the linking of (l - 2)-spheres and l-tori in the (2l - 1)-sphere.

Original languageEnglish (US)
Pages (from-to)351-356
Number of pages6
JournalEuropean Journal of Combinatorics
Volume13
Issue number5
DOIs
StatePublished - Sep 1992
Externally publishedYes

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ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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