Homology equivalences inducing an epimorphism on the fundamental group and Quillen’s plus construction
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- by José L. Rodríguez and Dirk Scevenels PDF
- Proc. Amer. Math. Soc. 132 (2004), 891-898 Request permission
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.References
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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
- 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
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 2019970