Abstract
A finitely presented group G is said to be properly 3-realizable if there exists a compact 2-polyhedron K with π1 (K) ≅ G whose universal cover has the proper homotopy type of a 3-manifold (with boundary). We discuss the behavior of this property with respect to amalgamated products, HNN-extensions, and direct products, as well as the independence with respect to the chosen 2-polyhedron. We also exhibit certain classes of groups satisfying this property: finitely generated Abelian groups, (classical) hyperbolic groups, and one-relator groups.
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