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

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

2003-01-28

arxiv.org/abs/math/0301328v1

Proc. AMS. 132, No.3, 891--898 (2004).

Mathematics

Algebraic Topology

12 pages. To appear in Proceedings of the AMS

Scientific paper

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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