2015/11/26 by Abbas Bahri, Bahri, A., Martin Bendersky +5
Computer Science · Mathematics · #55N10 #55N35 #55T25 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #K-Theory and Homology (math.KT) #Primary 55T05 #Secondary 52C35 #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1511.08292
openalex publication_date 2015/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is to exhibit fine structure for polyhedral products Z(K;(X,A) and polyhedral smash products \widehatZ(K;(X,A). (Moment-angle complexes are special cases for which (X,A) = (D2,S1)). There are three main parts. The first defines a natural filtration of the polyhedral product and derives properties of the resulting spectral sequence. This is followed with applications. The second part uses the first to give a homological decomposition of the polyhedral smash product. Finally there are applications to the ring structure of H*(Z(K;(X,A))) for CW-pairs (X,A) satisfying suitable freeness conditions.