## Simply connected quasiregularly elliptic 4-manifolds.(English)Zbl 1116.30011

An oriented and connected Riemannian manifold $$N$$ is named $$K$$-quasiregularly ellipitc if there exists a nonconstant $$K$$ quasiregular map of $$R^n$$ into $$N$$. Recently Bonk and Heinonen proved that being quasiregular elliptic imposes a bound on de Rham cohomology ring of $$N$$. In the paper under review it is shown that however the connected sum $$S^2 \times S^2 \# S^2 \times S^2$$ it is quasiregularly elliptic solving a question posed independently by Gromov and the author.

### MSC:

 30C65 Quasiconformal mappings in $$\mathbb{R}^n$$, other generalizations 57M12 Low-dimensional topology of special (e.g., branched) coverings
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