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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A class of manifolds covered by Euclidean space


Author: J. W. Maxwell
Journal: Proc. Amer. Math. Soc. 46 (1974), 414-418
MSC: Primary 57C99
DOI: https://doi.org/10.1090/S0002-9939-1974-0348757-7
MathSciNet review: 0348757
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Abstract: The following is the main result:

Theorem 1. Suppose $ {W^n}$ is a PL manifold which has homotopy type $ K(\Pi ,1),W$ has one end $ \infty ,{\pi _1}$ is essentially constant at $ \infty $, and the induced homomorphism $ {\pi _1}(\infty ) \to {\pi _1}(W)$ is an isomorphism. Then the universal cover of $ W$ is PL homomorphic to $ {R^n}$ provided $ n \geq 5$.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0348757-7
Keywords: Homotopy type $ K(\pi ,1)$, universal cover, euclidean space, end
Article copyright: © Copyright 1974 American Mathematical Society

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