Moment-Angle Manifolds Corresponding to Three-Dimensional Simplicial Spheres, Chordality, and Connected Sums of Products of Spheres
Abstract
We prove that the moment-angle complex $${\mathcal{Z}}_{\mathcal{K}}$$ corresponding to a $$3$$ -dimensional simplicial sphere $${\mathcal{K}}$$ has the cohomology ring isomorphic to the cohomology ring of a connected sum of products of spheres if and only if either (a) $${\mathcal{K}}$$ is the boundary of a $$4$$ -dimensional cross-polytope, or (b) the one-skeleton of $${\mathcal{K}}$$ is a chordal graph, or (c) there are only two missing edges in $${\mathcal{K}}$$ and they form a chordless $$4$$ -cycle. For simplicial spheres $${\mathcal{K}}$$ of arbitrary dimension, we obtain a sufficient condition for the ring isomorphism $$H^*(\mathcal Z_{\mathcal{K}})\cong H^*(M)$$ where $$M$$ is a connected sum of products of spheres.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Advanced Numerical Analysis Techniques
Point processes and geometric inequalities
Publication details
- Journal / source
- Mathematical Notes
- Publisher
- Pleiades Publishing Ltd
- Volume
- 119
- Issue
- 1-2
- Pages
- 70–81
- Publication date
- 1 February 2026
- Language
- EN