Abstract
Let φ : Z / p → GL n ( Z ) denote an integral representation of the cyclic group of prime order p. This induces a Z / p -action on the torus X = R n / Z n . The goal of this paper is to explicitly compute the cohomology groups H ⁎ ( X / Z / p ; Z ) for any such representation. As a consequence we obtain an explicit calculation of the integral cohomology of the classifying space associated to the family of finite subgroups for any crystallographic group Γ = Z n ⋊ Z / p with prime holonomy.
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