Degenerate Fibres in the Stone-čech Compactification of the Universal Bundle of a Finite Group
نویسنده
چکیده
Applied to a continuous surjection π : E → B of completely regular Hausdorff spaces E and B, the Stone-Čech compactification functor β yields a surjection βπ : βE → βB. For an n-fold covering map π, we show that the fibres of βπ, while never containing more than n points, may degenerate to sets of cardinality properly dividing n. In the special case of the universal bundle π : EG → BG of a p-group G, we show more precisely that every possible type of G-orbit occurs among the fibres of βπ. To prove this, we use a weak form of the so-called generalized Sullivan conjecture.
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Degenerate fibres in the Stone - Čech compactification of the universal bundle of a finite group : An application of homotopy theory to general topology
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