Knowledge of the Hurewicz image can go a long way toward determining the homotopy type of a finite CW-complex or its loop space. In this talk, we will show that the Hurewicz image for a moment-angle complex is closed under the sweep action in homology induced by the standard torus action and, in particular, contains the linear strand of the Stanley-Reisner ring. Combined with variants of a theorem of Eagon and Reiner well-known to commutative algebraists, we describe how this recovers results of various authors identifying the homotopy type of the moment-angle complex, its loop space and the map to its Davis-Januszkiewicz space for certain classes of simplicial complexes. Going further, we introduce a large class of Gorenstein complexes which generalizes the homological behaviour of cyclic and stacked polytopes, and of certain neighbourly sphere triangulations. For these simplicial complexes, we show that the associated moment-angle complexes have the rational homotopy type of connected sums of sphere products and the (integral) loop space homotopy type of products of loops on spheres.

This is joint work with Ben Briggs.