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

Assaf Libman. "Orbit spaces, Quillen's Theorem A and Minami's formula for compact Lie groups." Fundamenta Mathematicae 213.2 (2011): 115-167. <http://eudml.org/doc/282927>.

@article{AssafLibman2011,
abstract = {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.},
author = {Assaf Libman},
journal = {Fundamenta Mathematicae},
keywords = {homology decomposition; compact Lie group; subgroup complexes; Quillen Theorem A; Minami formula},
language = {eng},
number = {2},
pages = {115-167},
title = {Orbit spaces, Quillen's Theorem A and Minami's formula for compact Lie groups},
url = {http://eudml.org/doc/282927},
volume = {213},
year = {2011},
}

TY - JOUR
AU - Assaf Libman
TI - Orbit spaces, Quillen's Theorem A and Minami's formula for compact Lie groups
JO - Fundamenta Mathematicae
PY - 2011
VL - 213
IS - 2
SP - 115
EP - 167
AB - 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.
LA - eng
KW - homology decomposition; compact Lie group; subgroup complexes; Quillen Theorem A; Minami formula
UR - http://eudml.org/doc/282927
ER -