What question did this study set out to answer?

The research aims to construct a simplicial 4-sphere whose moment-angle manifold incorporates an arbitrary finitely generated abelian group in its homological structure.

February 21, 2026International Mathematics Research Notices

Moment Angle Manifolds Corresponding to S 4 Whose Homology and Loop Homology May Have Arbitrary Torsion

View Full Paper

Ask AI

Bookmark

The research aims to construct a simplicial 4-sphere whose moment-angle manifold incorporates an arbitrary finitely generated abelian group in its homological structure.
Constructed a simplicial 4-sphere
Analyzed the associated moment-angle manifold
Examined homological properties with respect to finitely generated abelian groups
The moment-angle manifold's homology contains the group G as a subgroup
The loop homology also includes G, demonstrating its presence in both structures

Implication

Demonstrates that moment-angle manifolds can include arbitrary torsion in homology with finite abelian groups.

Abstract

Let G be an arbitrary finitely generated abelian group, we prove that there exists a simplicial $4$-sphere whose associated moment-angle manifold has the property that both its homology and its loop homology contain G as a subgroup.

Discussion

No takes yet. Share an insight, caveat, or question.

Cite This Study

Han et al. (2026) studied this question.

synapsesocial.com/papers/69994cdf873532290d021c62 https://doi.org/10.1093/imrn/rnag024

View Full Paper

Ask AI

Bookmark

Implication

Demonstrates that moment-angle manifolds can include arbitrary torsion in homology with finite abelian groups.

Moment Angle Manifolds Corresponding to S 4 Whose Homology and Loop Homology May Have Arbitrary Torsion

Key Points

Implication

Abstract

Discussion

Cite This Study

Moment Angle Manifolds Corresponding to S 4 Whose Homology and Loop Homology May Have Arbitrary Torsion

Key Points

Implication

Abstract

Discussion

Cite This Study

Keep reading

Keep reading