Whitehead products in moment-angle complexes

Abstract

In toric topology, to a simplicial complex 𝐾 with 𝑚 vertices, one associates two spaces, the moment-angle complex 𝒵_𝐾 and the Davis–Januszkiewicz space 𝐷𝐽_𝐾. These spaces are connected by a homotopy fibration 𝒵_𝐾 → 𝐷𝐽_𝐾 → (ℂ𝑃^∞)^𝑚. In this paper, we show that the map 𝒵_𝐾 → 𝐷𝐽_𝐾 is identified with a wedge of iterated (higher) Whitehead products for a certain class of simplicial complexes 𝐾 including dual shellable complexes. We will prove the result in a more general setting of polyhedral products.