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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Degenerate fibres in the Stone-Cech compactification of the universal bundle of a finite group


Authors: David Feldman and Alexander Wilce
Journal: Trans. Amer. Math. Soc. 354 (2002), 3757-3769
MSC (2000): Primary 54D35, 55R35
Published electronically: April 23, 2002
MathSciNet review: 1911520
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Abstract: Applied to a continuous surjection $\pi : E \rightarrow B$ of completely regular Hausdorff spaces $E$ and $B$, the Stone-Cech compactification functor $\beta$ yields a surjection $\beta \pi: \beta E \rightarrow \beta B$. For an $n$-fold covering map $\pi$, we show that the fibres of $\beta \pi$, while never containing more than $n$ points, may degenerate to sets of cardinality properly dividing $n$. In the special case of the universal bundle $\pi:EG \rightarrow BG$ of a $p$-group $G$, we show more precisely that every possible type of $G$-orbit occurs among the fibres of $\beta \pi$. To prove this, we use a weak form of the so-called generalized Sullivan conjecture.


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Additional Information

David Feldman
Affiliation: Department of Mathematics, University of New Hampshire, Durham, New Hampshire 03824
Email: David.Feldman@unh.edu

Alexander Wilce
Affiliation: Department of Mathematics and Computer Science, Juniata College, Huntingdon, Pennsylvania 16652
Address at time of publication: Department of Mathematical Sciences, Susquehanna University, Selinsgrove, PA 17870
Email: wilce@juniata.edu, wilce@susqu.edu

DOI: https://doi.org/10.1090/S0002-9947-02-03008-8
Received by editor(s): January 1, 2002
Published electronically: April 23, 2002
Article copyright: © Copyright 2002 American Mathematical Society