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Homotopy decompositions of orbit spaces and the Webb conjecture

Jolanta Słomińska (2001)

Fundamenta Mathematicae

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 E . . . N E ) defined over the poset ( s d p ( G ) ) / G , where sd is the barycentric subdivision. We also...

Homotopy representability of Brauer groups.

Antonio Martínez Cegarra (1999)

Extracta Mathematicae

The purpose of this paper is to present certain facts and results showing a way through which simplicial homotopy theory can be used in the study of Auslander-Goldman-Brauer groups of Azumaya algebras over commutative rings.

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