On the algebra associated with a geometric lattice

Michael Falk

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


Let L be a geometric lattice. Following P. Orlik and L. Solomon, Combinatorics and topology of complements of hyperplanes, Invent. math. 56 (1980), 167-189, we associate with L a graded commutative algebra A(L). In this paper we introduce a new invariant ψ of the algebra A(L) which suffices to distinguish algebras for which all other known invariants coincide. This result is applied to the study of arrangements of complex hyperplanes, with L being the intersection lattice. In this case A(L) is isomorphic to the cohomology algebra of the associated hyperplane complement. The goal is to find examples of arrangements with non-isomorphic lattices but homotopy equivalent complements. The invariant introduced here effectively narrows the list of candidates. Nevertheless, we exhibit combinatorially inequivalent arrangements for which all known invariants, including ψ, coincide.

Original languageEnglish (US)
Pages (from-to)152-163
Number of pages12
JournalAdvances in Mathematics
Issue number2
StatePublished - Apr 1990

ASJC Scopus subject areas

  • General Mathematics


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