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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2001 | 169 | 3 | 249-287

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

EN

### Abstrakty

EN
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 → 𝓢(G) we construct a natural G-map $hocolim_{𝒲_{d}}G/d(-) → |W|$ which is a (non-equivariant) homotopy equivalence, hence $hocolim_{𝒲_{d}}EG × _GF_{d} → EG ×_G |W|$ 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 $𝒲_{d}$; 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: 𝓒 → 𝒪(G) into the category of G-orbits which guarantees that the associated map $α_F: hocolim_{𝓒} EG ×_G F(-) → BG$ is a mod-p-homology decomposition.

249-287

wydano
2001

### Twórcy

autor
• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
autor
• Faculty of Mathematics and Information Sciences, Warsaw Technical University, Pl. Politechniki 1, 00-661 Warszawa, Poland