In the paper we investigate continuity of Orlicz–Sobolev mappings W1,P(M,N)\documentclass[12pt]{minimal}
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\begin{document}$$W^{1,P}(M,N)$$\end{document} of finite distortion between smooth Riemannian n-manifolds, n≥2\documentclass[12pt]{minimal}
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\begin{document}$$n\ge 2$$\end{document}, under the assumption that the Young function P satisfies the so-called divergence condition ∫1∞P(t)/tn+1dt=∞\documentclass[12pt]{minimal}
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\begin{document}$$\int _1^\infty P(t)/t^{n+1}\, \hbox {d}t=\infty $$\end{document}. 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 Df∈Ln\documentclass[12pt]{minimal}
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\begin{document}$$Df\in L^n$$\end{document} and, more generally, mappings with Df∈Lnlog-1L\documentclass[12pt]{minimal}
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\begin{document}$$Df\in L^n\log ^{-1}L$$\end{document}. On the other hand, if the space W1,P\documentclass[12pt]{minimal}
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\begin{document}$$W^{1,P}$$\end{document} is larger than W1,n\documentclass[12pt]{minimal}
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\begin{document}$$W^{1,n}$$\end{document} (for example if Df∈Lnlog-1L\documentclass[12pt]{minimal}
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\begin{document}$$Df\in L^n\log ^{-1}L$$\end{document}), and the universal cover of N is homeomorphic to Sn\documentclass[12pt]{minimal}
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\begin{document}$$\mathbb {S}^n$$\end{document}, n≠4\documentclass[12pt]{minimal}
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\begin{document}$$n\ne 4$$\end{document}, or is diffeomorphic to Sn\documentclass[12pt]{minimal}
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\begin{document}$$\mathbb {S}^n$$\end{document}, n=4\documentclass[12pt]{minimal}
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\begin{document}$$n=4$$\end{document}, then we construct an example of a mapping in W1,P(M,N)\documentclass[12pt]{minimal}
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\begin{document}$$W^{1,P}(M,N)$$\end{document} 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.
