On the moment-angle manifold constructed by Fan, Chen, Ma and Wang

TL;DR

This paper proves that a specific class of moment-angle manifolds constructed by Fan, Chen, Ma, and Wang are actually diffeomorphic, confirming their topological equivalence beyond cohomology ring isomorphism.

Contribution

The paper establishes the diffeomorphism of moment-angle manifolds previously known to have isomorphic cohomology rings, providing a stronger topological classification.

Findings

Moment-angle manifolds are diffeomorphic to connected sums of sphere products.

Cohomology ring isomorphism implies diffeomorphism in this case.

Supports the conjecture that certain topological invariants determine manifold classification.

Abstract

Fan, Chen, Ma and Wang constructed a moment-angle manifold $Z_K$ whose cohomology ring is isomorphic to that of a connected sum of sphere products with one product of three spheres. In this paper, we show that they are actually diffeomorphic.