Surgery spaces of crystallographic groups

Abstract

Let Γ be a crystallographic group acting on the n-dimensional Euclidean space. In this dissertation, the surgery obstruction groups of Γ are computed in terms of certain sheaf homology groups defined by F. Quinn, when Γ has no 2-torsion. The main theorem is :

Theorem : If a crystallographic group Γ has no 2-torsion, there is a natural isomorphism

a : H_*(Rⁿ /Γ; L(p)) → L_*^-∞(Γ).