### Maps between classifying spaces.

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We are interested in a topological realization of a family of pseudoreflection groups $G\subset GL(n,{F}_{p})$; i.e. we are looking for topological spaces whose mod-p cohomology is isomorphic to the ring of invariants ${F}_{p}{[{x}_{1},...,{x}_{n}]}^{G}$. Spaces of this type give partial answers to a problem of Steenrod, namely which polynomial algebras over ${F}_{p}$ 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 $\mathbb{Z}/q\wr {\Sigma}_{n}$ where q divides p - 1 and where p is...

We obtain two classifications of weighted projective spaces: up to hoeomorphism and up to homotopy equivalence. We show that the former coincides with Al Amrani's classification up to isomorphism of algebraic varieties, and deduce the latter by proving that the Mislin genus of any weighted projective space is rigid.

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