Higher dimensional Peiffer elements in simplicial commutative algebras.
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 of the classifying space of the category associated to the G-poset 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 defined over the poset , where sd is the barycentric subdivision. We also...