I will discuss a work with Susanna Heikkilä (Jyväskylä) showing 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. This result imposes an algebraic restriction to existence of such entire mappings and leads to a homeomorphic classification of closed (simply connected) 4-manifolds which admit a quasiregular mapping from the Euclidean space. Interestingly this result is inspired by a similar result in uniformly quasiregular dynamics.