Abstract
AbstractLet Γ1 and Γ2 be Bieberbach groups contained in the full isometry group G of ℝn. We prove that if the compact flat manifolds Γ1\ℝn and Γ2\ℝn are strongly isospectral, then the Bieberbach groups Γ1 and Γ2 are representation equivalent; that is, the right regular representations L2(Γ1\G) and L2(Γ2\G) are unitarily equivalent.
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