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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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