Topological rigidity of quoric manifolds

Quoric manifolds are the quaternionic analogue of toric/quasitoric 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 homotopy equivalent to a quoric manifold is equivariantly homeomorphic to it. The proof is given by generalizing the methods used for Coxeter and quasitoric manifolds.