Degenerate fibres in the Stone-Cech compactification of the universal bundle of a finite group |
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Authors: | David Feldman Alexander Wilce |
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Affiliation: | Department of Mathematics, University of New Hampshire, Durham, New Hampshire 03824 ; Department of Mathematics and Computer Science, Juniata College, Huntingdon, Pennsylvania 16652 |
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Abstract: | Applied to a continuous surjection of completely regular Hausdorff spaces and , the Stone-Cech compactification functor yields a surjection . For an -fold covering map , we show that the fibres of , while never containing more than points, may degenerate to sets of cardinality properly dividing . In the special case of the universal bundle of a -group , we show more precisely that every possible type of -orbit occurs among the fibres of . To prove this, we use a weak form of the so-called generalized Sullivan conjecture. |
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