Topological obstructions to continuity of Orlicz-Sobolev mappings of finite distortion

In the paper we investigate continuity of Orlicz-Sobolev mappings W1,P(M,N) of finite distortion between smooth Riemannian n-manifolds, n2, under the assumption that the Young function P satisfies the so-called divergence condition 1P(t)/tn+1dt=. We prove that if the manifolds are oriented, N is compact, and the universal cover of N is not a rational homology sphere, then such mappings are continuous. That includes mappings with DfLn and, more generally, mappings with DfLnlog-1L. On the other hand, if the space W1,P is larger than W1,n (for example if DfLnlog-1L), and the universal cover of N is homeomorphic to Sn, n4, or is diffeomorphic to Sn, n=4, then we construct an example of a mapping in W1,P(M,N) that has finite distortion and is discontinuous. This demonstrates a new global-to-local phenomenon: Both finite distortion and continuity are local properties, but a seemingly local fact that finite distortion implies continuity is a consequence of a global topological property of the target manifold N.