Homotopy rigidity for quasitoric manifolds over a product of $d$-simplices

TL;DR

This paper proves that quasitoric manifolds over a product of d-simplices are homotopy equivalent after localization if their cohomology rings are isomorphic, revealing a rigidity property in their topological classification.

Contribution

It establishes a homotopy rigidity result for quasitoric manifolds over products of d-simplices based on cohomology ring isomorphism.

Findings

Homotopy equivalence after localization for quasitoric manifolds with isomorphic cohomology rings.

Homotopy rigidity holds over products of d-simplices.

Cohomology ring isomorphism implies homotopy equivalence in this setting.

Abstract

For a fixed integer $d\geq 1$, we show that two quasitoric manifolds over a product of $d$-simplices are homotopy equivalent after appropriate localization, provided that their integral cohomology rings are isomorphic.