# A moment-angle manifold whose cohomology is not torsion free

## TL;DR

This paper presents a method to construct moment-angle manifolds with cohomology containing torsion, and describes the associated simplicial sphere via its non-faces, advancing understanding of their topological properties.

## Contribution

It introduces a novel construction technique for moment-angle manifolds with torsion in cohomology and provides a way to describe the related simplicial sphere.

## Key findings

- Constructed explicit examples of moment-angle manifolds with torsion cohomology
- Developed a method to describe simplicial spheres by their non-faces
- Enhanced understanding of the topological complexity of moment-angle manifolds

## Abstract

In this paper we give a method to construct moment-angle manifolds whose cohomologies are not torsion free. We also give method to describe the corresponding simplicial sphere by its non-faces.