Higher Whitehead products in toric topology

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.

This version is as of March 2014. Several corrections made from the first submission

References in corpus (2)

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

Cited by in corpus (6)

• Higher order Whitehead products and $L_{\infty }$ structures on the homology of a DGL
• Polyhedral products for shifted complexes and higher Whitehead products
• Whitehead products in moment-angle complexes
• Decompositions of looped co-H-spaces and applications
• The homotopy type of the polyhedral product for shifted complexes
• On the higher order exterior and interior Whitehead products