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

• Autorzy: Stefan Jackowski , Jolanta Słomińska
• Języki publikacji: 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.

Kategorie tematyczne

• 55R35: Classifying spaces of groups and H -spaces
• 55U99: None of the above, but in this section
• 18G99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 169
• Numer: 3
• Strony: 249-287

Daty

wydano

2001

Twórcy

autor

Stefan Jackowski

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland

autor

Jolanta Słomińska

• Faculty of Mathematics and Information Sciences, Warsaw Technical University, Pl. Politechniki 1, 00-661 Warszawa, Poland

Identyfikatory

DOI

10.4064/fm169-3-4