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

• Autorzy: Assaf Libman
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 55R35: Classifying spaces of groups and H -spaces
• 22E99: None of the above, but in this section
• 55N91: Equivariant homology and cohomology
• 55U40: Topological categories, foundations of homotopy theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 213
• Numer: 2
• Strony: 115-167

Daty

wydano

2011

Twórcy

autor

Assaf Libman

• Department of Mathematical Sciences, King's College, University of Aberdeen, Aberdeen AB24 3UE, Scotland, U.K.

Identyfikatory

DOI

10.4064/fm213-2-2