Polyhedral products associated to pseudomanifolds

Abstract

We study the homotopy theory of polyhedral products associated to a combinatorial generalisation of manifolds known as pseudomanifolds. As special cases, we show that loop spaces of moment-angle manifolds associated to triangulations of $S^2$ and $S^3$ decompose as a product of spheres and loops on spheres.

19 pages, generalised some results thanks to referee comments, version accepted by International Mathematics Research Notices