ALEXANDER r-TUPLES AND BIER COMPLEXES

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4 Scopus citations

Abstract

We introduce and study Alexander r-tuples K = <K-i >(r)(i=1) of simplicial complexes, as a common generalization of pairs of Alexander dual complexes (Alexander 2-tuples) and r-unavoidable complexes of [3] and [11]. In the same vein, the Bier complexes, defined as the deleted joins K-Delta*of Alexander r-tuples, include both standard Bier spheres and optimal multiple chessboard complexes (Section 2.2) as interesting, special cases.

Our main results are Theorem 4.1 saying that (1) the r-fold deleted join of Alexander r-tuple is a pure complex homotopy equivalent to a wedge of spheres, and (2) the r-fold deleted join of a collective unavoidable r-tuple is (n - r - 1)-connected, and a classification theorem (Theorem 5.1 and Corollary 5.1) for Alexander r-tuples and Bier complexes.

Translated title of the contributionАлександеровские r-наборы и Бировы комплексы
Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalPublications de l'Institut Mathematique
Volume104
Issue number118
DOIs
StatePublished - 2018

Scopus subject areas

  • Mathematics(all)

Keywords

  • Bier spheres
  • Alexander duality
  • chessboard complexes
  • unavoidable complexes
  • discrete Morse theory
  • SPHERES

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