Discrete Morse theory for moment-angle complexes of pairs (Dⁿ,S^n-1)

2012/12/10 by Vladimir Grujić, Grujic, Vladimir, Volkmar Welker +1 · 1 citation
Chemistry · Computer Science · Mathematics · #05E45 #55P15 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Molecular spectroscopy and chirality #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1212.2028

openalex publication_date 2012/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a finite simplicial complex K and a CW-pair (X,A), there is an associated CW-complex Z_K(X,A), known as a polyhedral product. We apply discrete Morse theory to a particular CW-structure on the n-sphere moment-angle complexes Z_K(Dⁿ, S^n-1). For the class of simplicial complexes with vertex-decomposable duals, we show that the associated n-sphere moment-angle complexes have the homotopy type of wedges of spheres. As a corollary we show that a sufficiently high suspension of any restriction of a simplicial complex with vertex-decomposable dual is homotopy equivalent to a wedge of spheres.

Citations

• The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces

Cited by

• Topology of polyhedral products and the Golod property of Stanley-Reisner rings

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• Iterated Higher Whitehead products in topology of moment-angle complexes
• Whitehead products in moment-angle complexes
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• The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces