$p$-local decompositions of looped polyhedral products

Abstract: We show that localised away from a finite set of primes, the loop space of a moment-angle complex is homotopy equivalent to a product of loops on spheres. This verifies a conjecture of Anick for such spaces. We also develop a method to reduce the study of the loops of more general polyhedral products to that of the loops on a moment-angle complex. As a consequence, we give $p$-local loop space decompositions of a wide family of polyhedral products, quasitoric manifolds and simply connected toric orbifolds. We also describe the additive structure of loop homology of simply connected polyhedral products in terms of polynomials studied by Backelin and Berglund.