G-functors, G-posets and homotopy decompositions of G-spaces

Stefan Jackowski, and Jolanta Słomińska. "G-functors, G-posets and homotopy decompositions of G-spaces." Fundamenta Mathematicae 169.3 (2001): 249-287. <http://eudml.org/doc/281643>.

@article{StefanJackowski2001,
abstract = {We describe a unifying approach to a variety of homotopy decompositions of classifying spaces, mainly of finite groups. For a group G acting on a poset W and an isotropy presheaf d:W → (G) we construct a natural G-map $hocolim_\{_\{d\}\}G/d(-) → |W|$ which is a (non-equivariant) homotopy equivalence, hence $hocolim_\{_\{d\}\}EG × _GF_\{d\} → EG ×_G |W|$ is a homotopy equivalence. Different choices of G-posets and isotropy presheaves on them lead to homotopy decompositions of classifying spaces. We analyze higher limits over the categories associated to isotropy presheaves $_\{d\}$; in some important cases they vanish in dimensions greater than the length of W and can be explicitly calculated in low dimensions. We prove a cofinality theorem for functors F: → (G) into the category of G-orbits which guarantees that the associated map $α_F: hocolim_\{\} EG ×_G F(-) → BG$ is a mod-p-homology decomposition.},
author = {Stefan Jackowski, Jolanta Słomińska},
journal = {Fundamenta Mathematicae},
keywords = {-orbits},
language = {eng},
number = {3},
pages = {249-287},
title = {G-functors, G-posets and homotopy decompositions of G-spaces},
url = {http://eudml.org/doc/281643},
volume = {169},
year = {2001},
}

TY - JOUR
AU - Stefan Jackowski
AU - Jolanta Słomińska
TI - G-functors, G-posets and homotopy decompositions of G-spaces
JO - Fundamenta Mathematicae
PY - 2001
VL - 169
IS - 3
SP - 249
EP - 287
AB - We describe a unifying approach to a variety of homotopy decompositions of classifying spaces, mainly of finite groups. For a group G acting on a poset W and an isotropy presheaf d:W → (G) we construct a natural G-map $hocolim_{_{d}}G/d(-) → |W|$ which is a (non-equivariant) homotopy equivalence, hence $hocolim_{_{d}}EG × _GF_{d} → EG ×_G |W|$ is a homotopy equivalence. Different choices of G-posets and isotropy presheaves on them lead to homotopy decompositions of classifying spaces. We analyze higher limits over the categories associated to isotropy presheaves $_{d}$; in some important cases they vanish in dimensions greater than the length of W and can be explicitly calculated in low dimensions. We prove a cofinality theorem for functors F: → (G) into the category of G-orbits which guarantees that the associated map $α_F: hocolim_{} EG ×_G F(-) → BG$ is a mod-p-homology decomposition.
LA - eng
KW - -orbits
UR - http://eudml.org/doc/281643
ER -