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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Homology equivalences inducing an epimorphism on the fundamental group and Quillen's plus construction


Authors: José L. Rodríguez and Dirk Scevenels
Journal: Proc. Amer. Math. Soc. 132 (2004), 891-898
MSC (2000): Primary 55P60, 55N15; Secondary 18A20, 18A40
Published electronically: October 21, 2003
MathSciNet review: 2019970
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Abstract: Quillen's plus construction is a topological construction that kills the maximal perfect subgroup of the fundamental group of a space without changing the integral homology of the space. In this paper we show that there is a topological construction that, while leaving the integral homology of a space unaltered, kills even the intersection of the transfinite lower central series of its fundamental group. Moreover, we show that this is the maximal subgroup that can be factored out of the fundamental group without changing the integral homology of a space.


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Additional Information

José L. Rodríguez
Affiliation: Área de Geometría y Topología, CITE III, Universidad de Almería, E–04120 La Cañada de San Urbano, Almería, Spain
Email: jlrodri@ual.es

Dirk Scevenels
Affiliation: Departement Wiskunde, Katholieke Universiteit Leuven Celestijnenlaan 200 B, B–3001 Heverlee, Belgium
Email: dirk.scevenels@wis.kuleuven.ac.be

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07221-6
PII: S 0002-9939(03)07221-6
Received by editor(s): July 29, 2002
Published electronically: October 21, 2003
Additional Notes: The first author was supported by the Spanish DGES grant PB97-0202
Communicated by: Paul Goerss
Article copyright: © Copyright 2003 American Mathematical Society