$p$-local stable cohomological rigidity of quasitoric manifolds

TL;DR

This paper proves that for quasitoric manifolds of certain dimensions, isomorphic cohomology rings imply identical $p$-local stable homotopy types, revealing a rigidity property in their topological structure.

Contribution

It establishes a $p$-local stable cohomological rigidity result for quasitoric manifolds of dimension up to $2p^2-4$, linking cohomology ring isomorphisms to homotopy types.

Findings

Cohomology ring isomorphism implies $p$-local stable homotopy equivalence for specified quasitoric manifolds.

Dimension bound of $2p^2-4$ is critical for the rigidity result.

The result applies to manifolds with dimension constraints related to prime $p$.

Abstract

It is proved that if two quasitoric manifolds of dimension $\le 2p^2-4$ for a prime $p$ have isomorphic cohomology rings, then they have the same $p$-local stable homotopy type.