## Duke Mathematical Journal

### Slow quasiregular mappings and universal coverings

Pekka Pankka

#### Abstract

We define slow quasiregular mappings and study cohomology and universal coverings of closed manifolds receiving slow quasiregular mappings. We show that closed manifolds receiving a slow quasiregular mapping from a punctured ball have the de Rham cohomology type of either $\mathbb{S}^n$ or $\mathbb{S}^{n-1}\times \mathbb{S}^1$. We also show that in the case of manifolds of the cohomology type of $\mathbb{S}^{n-1}\times \mathbb{S}^1$, the universal covering of the manifold has exactly two ends, and the lift of the slow mapping into the universal covering has a removable singularity at the point of punctuation. We also obtain exact growth bounds and a global homeomorphism–type theorem for slow quasiregular mappings into the manifolds of the cohomology type $\mathbb{S}^{n-1}\times \mathbb{S}^1$

#### Article information

Source
Duke Math. J., Volume 141, Number 2 (2008), 293-320.

Dates
First available in Project Euclid: 17 January 2008

https://projecteuclid.org/euclid.dmj/1200601793

Digital Object Identifier
doi:10.1215/S0012-7094-08-14123-7

Mathematical Reviews number (MathSciNet)
MR2376816

Zentralblatt MATH identifier
1140.30010

#### Citation

Pankka, Pekka. Slow quasiregular mappings and universal coverings. Duke Math. J. 141 (2008), no. 2, 293--320. doi:10.1215/S0012-7094-08-14123-7. https://projecteuclid.org/euclid.dmj/1200601793

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