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We study the homotopy types of moment-angle complexes, or equivalently, ofcomplements of coordinate subspace arrangements. The overall aim is to identifythe simplicial complexes K for which the corresponding moment-angle complex Z_Khas the homotopy type of a wedge of spheres or a connected sum of sphereproducts. When K is flag, we identify in algebraic and combinatorial termsthose K for which Z_K is homotopy equivalent to a wedge of spheres, and give acombinatorial formula for the number of spheres in the wedge. This extendsresults of Berglund and Joellenbeck on Golod rings and homotopy theoreticalresults of the first and third authors. We also establish a connection betweenminimally non-Golod rings and moment-angle complexes Z_K which are homotopyequivalent to a connected sum of sphere products. We go on to show that for anyflag complex K the loop spaces of Z_K and DJ(K) are homotopy equivalent to aproduct of spheres and loops on spheres when localised rationally or at any oddprime.

Homotopy types of moment-angle complexes for flag complexes