Loops on polyhedral products and diagonal arrangements

Abstract

In this paper we establish a connection between the loop space homology of the generalization of wedge defined by a simplicial complex K (so called polyhedral product) and the homology of certain diagonal arrangements associated with K. We illustrate these results by finding the presentations of those loop homology algebras for certain K generalizing results of Panov-Ray, Papadima-Suciu, Lemaire. Finally, we show that in the case when the functor is applied to suspensions, this homology splitting comes from the stable homotopy splitting of the loop spaces.

32 pages

References in corpus (2)

• Algebraic invariants for right-angled Artin groups
• The polyhedral product functor: a method of computation for moment-angle complexes, arrangements and related spaces