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Direct products and properly 3-realisable groups

Published online by Cambridge University Press:  17 April 2009

Manuel Cárdenas ,
Francisco F. Lasheras  and
Ranja Roy
Manuel Cárdenas
Affiliation:
Departamento de Geometría y Topología, Universidad de Sevilla, Apdo 1160, 41080-Sevilla, Spain e-mail: lasheras@us.es, mcard@us.es
Francisco F. Lasheras
Affiliation:
Departamento de Geometría y Topología, Universidad de Sevilla, Apdo 1160, 41080-Sevilla, Spain e-mail: lasheras@us.es, mcard@us.es
Ranja Roy
Affiliation:
New York Institute of Technology, Old Westbury, NY 11568–8000, United States of America e-mail: rroy@nyit.edu
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In this paper, we show that the direct of infinite finitely presented groups is always properly 3-realisable. We also show that classical hyperbolic groups are properly 3-realisable. We recall that a finitely presented group G is said to be properly 3-realisable if there exists a compact 2-polyhedron K with π1 (K) ≅ G and whose universal cover has the proper homotopy type of a (p.1.) 3-manifold with boundary. The question whether or not every finitely presented is properly 3-realisable remains open.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 2 , October 2004 , pp. 199 - 205
Copyright
Copyright © Australian Mathematical Society 2004

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