Minimally Non-Golod Simplicial Complexes and Moment-angle Manifolds Seminar

In 2007 A.Berglund and M.Jollenbeck introduced the notion of a minimally non-Golod face ring of a simplicial complex over a field (or the ring of integers). Namely, the face ring is not Golod itself but deleting of any vertex from the simplicial complex turns the face ring into a Golod one. In my talk I will consider mainly the case when the complex is a polytopal triangulated sphere and its face ring is minimally non-Golod. The latter property is preserved by certain simplicial operations performed on the complex. For many of the corresponding simple polytopes (among them are vertex truncations of one or a product of two simplices as well as dual neighbourly polytopes different from simplices and etc.) a description of the

diffeomorphism types of their moment-angle manifolds is well known in toric topology. These manifolds are connected sums of sphere products with two spheres in each product.