Polyhedral products for simplicial complexes with minimal Taylor resolutions

2015/06/05 by Iriye, Kouyemon, Kishimoto, Daisuke
#13F55 #55P15 #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1506.01759

Abstract

We prove that for a simplicial complex K whose Taylor resolution for the Stanley-Reisner ring is minimal, the following four conditions are equivalent: (1) K satisfies the strong gcd-condition; (2) K is Golod; (3) the moment-angle complex Z_K is homotopy equivalent to a wedge of spheres; (4) the decomposition of the suspension of the polyhedral product Z_K(C\underlineX,\underlineX) due to Bahri, Bendersky, Cohen, and Gitler desuspends.

Related

• Topology of polyhedral products and the Golod property of Stanley-Reisner rings
• Wedge decomposition of polyhedral products
• The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces
• Polyhedral products and features of their homotopy theory
• Three simplicial resolutions