On the Genera of Moment-Angle Manifolds Associated with Dual-Neighborly Polytopes: Combinatorial Formulas and Sequences

For a family of polytopes of even dimension 2p, known as dual-neighborly, it has been shown for \(p\ne 2\) that the associated intersection of quadrics is a connected sum of sphere products \(S^p\times S^p\) . In this article, we give formulas for the number of terms in that connected sum. Certain combinatorial operations produce new polytopes whose associated intersections are also connected sums of sphere products, and we give also formulas for their number. These include a large amount of simple polytopes, including many odd-dimensional ones.