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October, 2014 Groups of uniform homeomorphisms of covering spaces
Tatsuhiko YAGASAKI
J. Math. Soc. Japan 66(4): 1227-1248 (October, 2014). DOI: 10.2969/jmsj/06641227


In this paper we deduce a local deformation lemma for uniform embeddings in a metric covering space over a compact manifold from the deformation lemma for embeddings of a compact subspace in a manifold. This implies the local contractibility of the group of uniform homeomorphisms of such a metric covering space under the uniform topology. Furthermore, combining with similarity transformations, this enables us to induce a global deformation property of groups of uniform homeomorphisms of metric spaces with Euclidean ends. In particular, we show that the identity component of the group of uniform homeomorphisms of the standard Euclidean $n$-space is contractible.


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Tatsuhiko YAGASAKI. "Groups of uniform homeomorphisms of covering spaces." J. Math. Soc. Japan 66 (4) 1227 - 1248, October, 2014.


Published: October, 2014
First available in Project Euclid: 23 October 2014

zbMATH: 1310.57043
MathSciNet: MR3272598
Digital Object Identifier: 10.2969/jmsj/06641227

Primary: 57S05
Secondary: 54E40 , 57N15 , 58D10

Keywords: Euclidean ends , group of uniform homeomorphisms , space of uniform embeddings , uniform topology

Rights: Copyright © 2014 Mathematical Society of Japan


Vol.66 • No. 4 • October, 2014
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