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

DOI:
https://doi.org/10.1090/S0002-9939-03-07221-6

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:
https://doi.org/10.1090/S0002-9939-03-07221-6

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