Splitting B (Z/p)n and BTn Via Modular Representation Theory.
We show that for n ≥ 3 the symplectic group Sp(n) is as a 2-compact group determined up to isomorphism by the isomorphism type of its maximal torus normalizer. This allows us to determine the integral homotopy type of Sp(n) among connected finite loop spaces with maximal torus.
We are interested in a topological realization of a family of pseudoreflection groups ; i.e. we are looking for topological spaces whose mod-p cohomology is isomorphic to the ring of invariants . Spaces of this type give partial answers to a problem of Steenrod, namely which polynomial algebras over can appear as the mod-p cohomology of a space. The family under consideration is given by pseudoreflection groups which are subgroups of the wreath product where q divides p - 1 and where p is...
It is shown that the classification of polynomial algebras over the mod p Steenrod algebra is an essentially different problem from the classification of polynomial algebras truncated at height greater than p over the Steenrod algebra.