Higher Whitehead products in toric topology

2010/11/09 by Jelena Grbić, Grbic, Jelena, Stephen Theriault +1 · 4 citations
Computer Science · Mathematics · #13F55 #52C35 #55P25 #55Q15 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1011.2133

openalex publication_date 2010/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the relationship between the moment-angle complex Z_k and the Davis-Januskiewicz space DJ(K) for a class of complexes K named missing-face complexes. If K has n vertices we consider the homotopy fibration sequence Z_k --> DJ(K) --> M where M is a product of n copies of infinite complex projective space. We observe that for such K, Z_k is homotopy equivalent to a wedge of spheres, and then show that under this equivalence the map Z_k --> DJ(K) is homotopic to a wedge sum of higher Whitehead products and iterated Whitehead products.

Citations

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

Cited by

• On the higher order exterior and interior Whitehead products
• Rational higher order Whitehead products of mapping spaces and defining systems
• Polyhedral products for shifted complexes and higher Whitehead products
• Decompositions of looped co-H-spaces and applications
• Whitehead products in moment-angle complexes

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• Whitehead products in moment-angle complexes
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• A generalization of the Davis-Januszkiewicz construction and applications to toric manifolds and iterated polyhedral products