Geodesic
Properly 3-realizable groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 95-103.

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A finitely presented group $G$ is said to be properly 3-realizable if there exists a compact 2-polyhedron $K$ with $\pi_1(K)\cong G$ and 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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M. Cardenas; F. F. Lasheras; A. Quintero. Properly 3-realizable groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 11 (2005) no. 4, pp. 95-103. http://geodesic.mathdoc.fr/item/FPM_2005_11_4_a7/

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