I will discuss a result that, if a closed manifold admits a quasiregular mapping from a Euclidean space, then the de Rham cohomology of the manifold embeds into a Euclidean exterior algebra as a subalgebra. As a consequence of this embedding we obtain a homeomorphic classification of closed simply connected 4-manifolds which admit a quasiregular mapping from the Euclidean space. This is joint work with Susanna Heikkilä (Helsinki).