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Properly  -realizable groups |
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| Authors: | R Ayala M Cá rdenas F F Lasheras A Quintero |
| Institution: | Departamento de Geometría y Topología, Universidad de Sevilla, Apdo 1160, 41080-Sevilla, Spain M. Cárdenas ; Departamento de Geometría y Topología, Universidad de Sevilla, Apdo 1160, 41080-Sevilla, Spain F. F. Lasheras ; Departamento de Geometría y Topología, Universidad de Sevilla, Apdo 1160, 41080-Sevilla, Spain ; Departamento de Geometría y Topología, Universidad de Sevilla, Apdo 1160, 41080-Sevilla, Spain |
| Abstract: | A finitely presented group  is said to be properly  -realizable if there exists a compact  -polyhedron  with  and whose universal cover  has the proper homotopy type of a (p.l.)  -manifold with boundary. In this paper we show that, after taking wedge with a  -sphere, this property does not depend on the choice of the compact  -polyhedron  with  . We also show that (i) all  -ended and  -ended groups are properly  -realizable, and (ii) the class of properly  -realizable groups is closed under amalgamated free products (HNN-extensions) over a finite cyclic group (as a step towards proving that  -ended groups are properly  -realizable, assuming  -ended groups are). |
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