Stanley Reisner rings of generalized truncation polytopes and their moment angle manifolds

Abstract

We consider simple polytopes P = vck(Δn1 × . . . × Δnr ) for n1 ≥ . . . ≥ nr ≥ 1, r ≥ 1, and k ≥ 0, that is, k-vertex cuts of a product of simplices, and call them generalized truncation polytopes. For these polytopes we describe the cohomology ring of the corresponding moment–angle manifold ZP and explore some topological consequences of this calculation. We also examine minimal non-Golodness for their Stanley–Reisner rings and relate it to the property of ZP being a connected sum of sphere products.