Authors: | Jojić, Duško Nekrasov, Ilya Panina, Gaiane Živaljević, Rade |
Title: | Alexander r-tuples and bier complexes | Journal: | Publications de l'Institut Mathematique | Volume: | 104 | Issue: | 118 | First page: | 1 | Last page: | 22 | Issue Date: | 1-Jan-2018 | Rank: | M24 | ISSN: | 0350-1302 | DOI: | 10.2298/PIM1818001J | Abstract: | We introduce and study Alexander r-tuples K = 〈K i 〉 i=1r 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 Δ* 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. |
Keywords: | Alexander duality | Bier spheres | Chessboard complexes | Discrete Morse theory | Unavoidable complexes | Publisher: | Mathematical Institute of the SASA | Project: | Russian Science Foundation, grant 16-11-10039 Geometry and Topology of Manifolds, Classical Mechanics and Integrable Dynamical Systems Topology, geometry and global analysis on manifolds and discrete structures |
Show full item record
SCOPUSTM
Citations
7
checked on Sep 7, 2024
Page view(s)
2
checked on Sep 7, 2024
Google ScholarTM
Check
Altmetric
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.