Homotopy decompositions of orbit spaces and the Webb conjecture

• Autorzy: Jolanta Słomińska
• Języki publikacji: 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.

Kategorie tematyczne

• 18G40: Spectral sequences, hypercohomology
• 55P91: Equivariant homotopy theory
• 55U40: Topological categories, foundations of homotopy theory
• 18G10: Resolutions; derived functors

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 169
• Numer: 2
• Strony: 105-137

Daty

wydano

2001

Twórcy

autor

Jolanta Słomińska

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

Identyfikatory

DOI

10.4064/fm169-2-2