Remarks on the classification of quasitoric manifolds up to equivariant homeomorphism

TL;DR

This paper provides criteria to determine when two quasitoric manifolds are equivariantly homeomorphic and applies these to classify such manifolds based on their cohomology rings.

Contribution

It introduces three new sufficient criteria for weak equivariant homeomorphism and uses them to classify quasitoric manifolds by their cohomology.

Findings

Three criteria for weak equivariant homeomorphism of quasitoric manifolds

Application of criteria to count homeomorphism types with fixed cohomology

Enhanced understanding of classification of quasitoric manifolds

Abstract

We give three sufficient criteria for two quasitoric manifolds (M,M') to be (weakly) equivariantly homeomorphic. We apply these criteria to count the weakly equivariant homeomorphism types of quasitoric manifolds with a given cohomology ring.