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

Stefan Jackowski; Jolanta Słomińska

Fundamenta Mathematicae (2001)

- Volume: 169, Issue: 3, page 249-287
- ISSN: 0016-2736

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topStefan 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 -

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