Quasiregular mappings to generalized manifolds

We establish the basic analytic and geometric properties of quasiregular maps f: ω → X, where ω ? ? ⁿ is a domain and X is a generalized n-manifold with a suitably controlled geometry. Generalizing the classical Väisälä and Poletsky inequalities, our main theorem shows that the path family method applies to these maps.