Homotopy decompositions of orbit spaces and the Webb conjecture

Jolanta Słomińska

Fundamenta Mathematicae, Tome 167 (2001), p. 105-137 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $(B_{p} (G)) / G$ of the classifying space of the category associated to the G-poset $_{p} (G)$ 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 $X^{E ₙ} / (N E ₀ \cap . . . \cap N E ₙ)$ defined over the poset $(s d_{p} (G)) / G$ , 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 $E G \times_{G} B_{p} (G) \to B G$ induced by the G-map $B_{p} (G) \to *$ is a mod p homology isomorphism.

Publié le : 2001-01-01

Zbl 0985.55010

EUDML-ID : urn:eudml:doc:281590

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     title = {Homotopy decompositions of orbit spaces and the Webb conjecture},
     journal = {Fundamenta Mathematicae},
     volume = {167},
     year = {2001},
     pages = {105-137},
     zbl = {0985.55010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm169-2-2}
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Jolanta Słomińska. Homotopy decompositions of orbit spaces and the Webb conjecture. Fundamenta Mathematicae, Tome 167 (2001) pp. 105-137. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm169-2-2/