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

Stefan Jackowski; Jolanta Słomińska

Fundamenta Mathematicae, Tome 167 (2001), p. 249-287 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $h o c o l i m_{_{d}} G / d (-) \to | W |$ which is a (non-equivariant) homotopy equivalence, hence $h o c o l i m_{_{d}} E G \times_{G} F_{d} \to E G \times_{G} | W |$ 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 $α_{F} : h o c o l i m_{} E G \times_{G} F (-) \to B G$ is a mod-p-homology decomposition.

Publié le : 2001-01-01

Zbl 0985.55012

EUDML-ID : urn:eudml:doc:281643

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     title = {G-functors, G-posets and homotopy decompositions of G-spaces},
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     year = {2001},
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Stefan Jackowski; Jolanta Słomińska. G-functors, G-posets and homotopy decompositions of G-spaces. Fundamenta Mathematicae, Tome 167 (2001) pp. 249-287. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm169-3-4/