Online Talk

One problem associated to polyhedral products is identifying their homotopy type. In the case of a moment-angle complex, work of various authors has identified families of simplicial complexes for which their corresponding moment-angle complex is homotopy equivalent to a wedge of spheres. In particular, this implies that after looping, the moment-angle complex is homotopy equivalent to a finite type product of spheres and loops on spheres. However, there are simplicial complexes for which their corresponding moment-angle complex before looping is not a wedge of spheres, yet after looping, they still decompose as a product of spheres and loops on spheres. In this talk, I will survey the current progress in this direction, and then expand the family of simplicial complexes for which such a decomposition of the loop space is known -  namely to include simplicial complexes which are the k-skeleton of a flag complex.