Topological rigidity of quoric manifolds

Quoric manifolds are the quaternionic analogue of toric/quasitoric manifolds. They admit a locally nice action of (S3)n and the quotient is a manifold with corners. We show that they satisfy equivariant rigidity. More precisely, any locally linear (S3)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.