Topological rigidity of quoric manifolds
Volume 179 / 2025
Colloquium Mathematicum 179 (2025), 1-19
MSC: Primary 57S25; Secondary 57R18, 20C99
DOI: 10.4064/cm9611-5-2025
Published online: 7 August 2025
Abstract
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.
