Loop space decompositions of moment-angle complexes associated to two dimensional simplicial complexes

Abstract

We show that the loop space of a moment-angle complex associated to a $2$-dimensional simplicial complex decomposes as a finite type product of spheres, loops on spheres, and certain indecomposable spaces which appear in the loop space decomposition of Moore spaces. We also give conditions on certain subcomplexes under which, localised away from sufficiently many primes, the loop space of a moment-angle complex decomposes as a finite type product of spheres and loops on spheres.

22 pages, expositional changes in response to referee comments. Accepted version of manuscript to appear in Proceedings of the Edinburgh Mathematical Society