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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 the dimension of infinite covers


Authors: W. G. Dwyer, S. Stolz and L. R. Taylor
Journal: Proc. Amer. Math. Soc. 124 (1996), 2235-2239
MSC (1991): Primary 55U15, 57P10
MathSciNet review: 1307514
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Abstract: We prove the following theorem and some generalizations.

Theorem.. Let $X$ be a connected CW complex which satisfies Poincaré duality of dimension $n\ge 4$. For any subgroup $H$ of $\pi _1(X)$, let $X_H$ denote the cover of $X$ corresponding to $H$. If $H$ has infinite index in $\pi _1(X)$, then $X_H$ is homotopy equivalent to an $(n-1)$-dimensional CW complex.


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Additional Information

W. G. Dwyer
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: dwyer.1@nd.edu

S. Stolz
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: stolz.1@nd.edu

L. R. Taylor
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: taylor.2@nd.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03250-9
PII: S 0002-9939(96)03250-9
Keywords: Infinite covers, dimension
Received by editor(s): May 10, 1994
Received by editor(s) in revised form: November 18, 1994
Additional Notes: Partially supported by the National Science Foundation.
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1996 American Mathematical Society