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 $$p_{1}(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.

Location: http://mech.math.msu.su/~fpm/eng/k05/k054/k05408h.htm

Last modified: November 28, 2005