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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2001 | 169 | 2 | 105-137

## Homotopy decompositions of orbit spaces and the Webb conjecture

EN

### Abstrakty

EN
Let p be a prime number. We prove that if G is a compact Lie group with a non-trivial p-subgroup, then the orbit space $(B𝓐_p(G))/G$ of the classifying space of the category associated to the G-poset $𝓐_p(G)$ of all non-trivial elementary abelian p-subgroups of G is contractible. This gives, for every G-CW-complex X each of whose isotropy groups contains a non-trivial p-subgroup, a decomposition of X/G as a homotopy colimit of the functor $X^{Eₙ}/(NE₀ ∩ ... ∩ NEₙ)$ defined over the poset $(sd𝓐_p(G))/G$, where sd is the barycentric subdivision. We also investigate some other equivariant homotopy and homology decompositions of X and prove that if G is a compact Lie group with a non-trivial p-subgroup, then the map $EG ×_G B𝓐_p(G) → BG$ induced by the G-map $B𝓐_p(G) → ∗$ is a mod p homology isomorphism.

105-137

wydano
2001

### Twórcy

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