Homotopy decompositions of orbit spaces and the Webb conjecture

Jolanta Słomińska. "Homotopy decompositions of orbit spaces and the Webb conjecture." Fundamenta Mathematicae 169.2 (2001): 105-137. <http://eudml.org/doc/281590>.

@article{JolantaSłomińska2001,
abstract = {Let p be a prime number. We prove that if G is a compact Lie group with a non-trivial p-subgroup, then the orbit space $(B_p(G))/G$ of the classifying space of the category associated to the G-poset $_p(G)$ of all non-trivial elementary abelian p-subgroups of G is contractible. This gives, for every G-CW-complex X each of whose isotropy groups contains a non-trivial p-subgroup, a decomposition of X/G as a homotopy colimit of the functor $X^\{Eₙ\}/(NE₀ ∩ ... ∩ NEₙ)$ defined over the poset $(sd_p(G))/G$, where sd is the barycentric subdivision. We also investigate some other equivariant homotopy and homology decompositions of X and prove that if G is a compact Lie group with a non-trivial p-subgroup, then the map $EG ×_G B_p(G) → BG$ induced by the G-map $B_p(G) → ∗$ is a mod p homology isomorphism.},
author = {Jolanta Słomińska},
journal = {Fundamenta Mathematicae},
keywords = {compact Lie group; -poset; -CW-complex; homology decompositions},
language = {eng},
number = {2},
pages = {105-137},
title = {Homotopy decompositions of orbit spaces and the Webb conjecture},
url = {http://eudml.org/doc/281590},
volume = {169},
year = {2001},
}

TY - JOUR
AU - Jolanta Słomińska
TI - Homotopy decompositions of orbit spaces and the Webb conjecture
JO - Fundamenta Mathematicae
PY - 2001
VL - 169
IS - 2
SP - 105
EP - 137
AB - Let p be a prime number. We prove that if G is a compact Lie group with a non-trivial p-subgroup, then the orbit space $(B_p(G))/G$ of the classifying space of the category associated to the G-poset $_p(G)$ of all non-trivial elementary abelian p-subgroups of G is contractible. This gives, for every G-CW-complex X each of whose isotropy groups contains a non-trivial p-subgroup, a decomposition of X/G as a homotopy colimit of the functor $X^{Eₙ}/(NE₀ ∩ ... ∩ NEₙ)$ defined over the poset $(sd_p(G))/G$, where sd is the barycentric subdivision. We also investigate some other equivariant homotopy and homology decompositions of X and prove that if G is a compact Lie group with a non-trivial p-subgroup, then the map $EG ×_G B_p(G) → BG$ induced by the G-map $B_p(G) → ∗$ is a mod p homology isomorphism.
LA - eng
KW - compact Lie group; -poset; -CW-complex; homology decompositions
UR - http://eudml.org/doc/281590
ER -