Moment-angle manifolds and connected sums of sphere products

TL;DR

This paper explores specific moment-angle manifolds with cohomology rings matching connected sums of sphere products, providing examples and analyzing their properties to deepen understanding of their topological structure.

Contribution

It introduces new examples of moment-angle manifolds with particular cohomology properties and discusses their general topological characteristics.

Findings

Constructed a 4-dimensional example of a moment-angle manifold with specified cohomology.

Showed that the cohomology ring can be isomorphic to a connected sum of sphere products.

Identified general properties of these moment-angle manifolds.

Abstract

This paper investigates the moment-angle manifolds whose cohomology ring is isomorphic to that of a connected sum of sphere products. We first give a example of moment-angle manifolds corresponding to a 4 dimentional simplicial polytope. It has the property that its cohomology ring is isomorphic to that of a connected sum of sphere products with one produt of thress spheres. Finally, we give some general properties of this kind of moment-angle manifolds.