The homotopy type of the polyhedral product for shifted complexes

2011/09/13 by Grbic, Jelena, Theriault, Stephen · 1 citation
#52C35 (Secondary) #55P15 (Primary) 13F55 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1109.2728

Abstract

We prove a conjecture of Bahri, Bendersky, Cohen and Gitler: if K is a shifted simplicial complex on n vertices, X₁,..., X_n are spaces and CX_i is the cone on X_i, then the polyhedral product determined by K and the pairs (CX_i,X_i) is homotopy equivalent to a wedge of suspensions of smashes of the X_i's. This generalises earlier work of the two authors in the special case where each X_i is a loop space. Connections are made to toric topology, combinatorics, and classical homotopy theory.

Cited by

• Homotopy types of moment-angle complexes associated to almost linear resolutions

Related

• Polyhedral coproducts
• Polyhedral products and features of their homotopy theory
• Polyhedral products for shifted complexes and higher Whitehead products
• Polyhedral products in abstract and motivic homotopy theory
• Loops on polyhedral products and diagonal arrangements