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## Fundamenta Mathematicae

2011 | 213 | 2 | 115-167
Tytuł artykułu

### Orbit spaces, Quillen's Theorem A and Minami's formula for compact Lie groups

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Let G be a compact Lie group. We present a criterion for the orbit spaces of two G-spaces to be homotopy equivalent and use it to obtain a quick proof of Webb's conjecture for compact Lie groups. We establish two Minami type formulae which present the p-localised spectrum $Σ^∞ BG₊$ as an alternating sum of p-localised spectra $Σ^∞ BH₊$ for subgroups H of G. The subgroups H are calculated from the collections of the non-trivial elementary abelian p-subgroups of G and the non-trivial p-radical subgroups of G. We also show that the Bousfield-Kan spectral sequences of the normaliser decompositions associated to these collections and to any p-local cohomology theory h* collapse at their E₂-pages to their vertical axes, and converge to h*(BG). An important tool is a topological version of Quillen's Theorem A which we prove.
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Tom
Numer
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115-167
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wydano
2011
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• Department of Mathematical Sciences, King's College, University of Aberdeen, Aberdeen AB24 3UE, Scotland, U.K.
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