FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2005, VOLUME 11, NUMBER 4, PAGES 95-103

Properly $3$-realizable groups

M. Cárdenas
F. F. Lasheras
A. Quintero

Abstract

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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 $$p₁(K) @ 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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Last modified: November 28, 2005