Polyhedral products for shifted complexes and higher Whitehead products

2015/05/19 by Kouyemon Iriye, Iriye, Kouyemon, Daisuke Kishimoto +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1505.04892

openalex publication_date 2015/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies the map between polyhedral products Z_K(C\underlineX,\underlineX)\toZ_K(Σ\underlineX,*) induced from the pinch maps (CX_i,X_i)→(ΣX_i,*), which is the higher order Whitehead product if K is the boundary of a simplex. When K is a shifted complex, a wedge decomposition of Z_K(C\underlineX,\underlineX) is given by the authors. Based on this decomposition, when K is shifted, the induced pinch map is explicitly described as a wedge of iterated Whitehead products each of which includes at most one higher product. As a corollary, the Jacobi identity of Whitehead products including higher products due to Hardie is generalized.

Citations

• Higher Whitehead products in toric topology

Related

• Relations among higher Whitehead maps
• Jacobi identity in polyhedral products
• The homotopy type of the polyhedral product for shifted complexes
• Whitehead products in moment-angle complexes
• Iterated Higher Whitehead products in topology of moment-angle complexes