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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On covering translations and homeotopy groups of contractible open $n$-manifolds


Author: Robert Myers
Journal: Proc. Amer. Math. Soc. 128 (2000), 1563-1566
MSC (1991): Primary 57M10; Secondary 57N10, 57N13, 57N15, 57N37, 57M60, 57S30
Published electronically: October 6, 1999
MathSciNet review: 1641077
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Abstract: This paper gives a new proof of a result of Geoghegan and Mihalik which states that whenever a contractible open $n$-manifold $W$ which is not homeomorphic to $\mathbf{R}^n$ is a covering space of an $n$-manifold $M$ and either $n \geq 4$ or $n=3$ and $W$ is irreducible, then the group of covering translations injects into the homeotopy group of $W$.


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Additional Information

Robert Myers
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Email: myersr@math.okstate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05163-1
PII: S 0002-9939(99)05163-1
Keywords: Contractible open manifold, covering space, homeotopy group, mapping class group
Received by editor(s): October 17, 1997
Received by editor(s) in revised form: July 10, 1998
Published electronically: October 6, 1999
Additional Notes: Research at MSRI is supported in part by NSF grant DMS-9022140.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society