Loop space decompositions of moment-angle complexes associated to flag complexes

Abstract

We prove that the loop space of the moment-angle complex associated to the $k$-skeleton of a flag complex belongs to the class $\mathcal{P}$ of spaces homotopy equivalent to a finite type product of spheres and loops on simply connected spheres. To do this, a general result showing $\mathcal{P}$ is closed under retracts is proved.

arXiv comment24 pages, Various changes in response to referee comments, including the filling of a gap in Section 3. Accepted version of manuscript to appear in The Quarterly Journal of Mathematics