Topological rigidity of quoric manifolds

TL;DR

This paper proves that quoric manifolds, quaternionic analogues of toric manifolds, are uniquely determined by their equivariant homotopy type, establishing a form of topological rigidity.

Contribution

It demonstrates that quoric manifolds satisfy equivariant rigidity, extending methods from Coxeter and toric manifolds to the quaternionic setting.

Findings

Quoric manifolds are equivariantly rigid under homotopy.

Any equivariant homotopy equivalence between quoric manifolds is an equivariant homeomorphism.

The proof generalizes techniques from toric and Coxeter manifold theory.

Abstract

Quoric manifolds are the quaternionic analogue of toric manifolds. They admit a locally nice action of $(S^3)^n$ and the quotient is a manifold with corners. We show that they satisfy equivariant rigidity. More precisely, any locally linear $(S^3)^n$-manifold that it is equivariantly homotopic equivalent to a quoric manifold is equivariantly homeomorphic to it. The proof is given by generalising the methods of used in Coxeter and toric manifolds.