Surgery spaces of crystallographic groups

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1982

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Virginia Polytechnic Institute and State University

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).

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