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Open aspherical manifolds not covered by the Euclidean space


Author: Igor Belegradek
Journal: Proc. Amer. Math. Soc. 143 (2015), 3641-3643
MSC (2010): Primary 57N15
DOI: https://doi.org/10.1090/proc/12308
Published electronically: April 6, 2015
MathSciNet review: 3348805
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Abstract: We show that any open aspherical manifold of dimension $ n\ge 4$ is tangentially homotopy equivalent to an $ n$-manifold whose universal cover is not homeomorphic to $ \mathbb{R}^n$.


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Additional Information

Igor Belegradek
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160
Email: ib@math.gatech.edu

DOI: https://doi.org/10.1090/proc/12308
Keywords: Aspherical manifold, homology sphere, hyperplane unknotting
Received by editor(s): October 20, 2012
Received by editor(s) in revised form: July 15, 2013
Published electronically: April 6, 2015
Additional Notes: The author is grateful for NSF support (DMS-1105045)
Communicated by: Kevin Whyte
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.