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Localization of seif-homotopy equivalences inducing the identity on homology

Published online by Cambridge University Press:  24 October 2008

Ken-Ichi Maruyama
Ken-Ichi Maruyama
Affiliation:
Department of Mathematics, Faculty of Education, Chiba University, Yayoicho, Chiba, Japan
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Extract

Let us denote the group of based homotopy classes of seif-homotopy equivalences of a space X by E(X). We consider E0(X), the subgroup of E(X) consisting of elements which induce the identity map on homology. Dror and Zabrodsky have shown that E0(X) and the subgroup E#(X) consisting of elements inducing the identity on homotopy are both nilpotent groups for finite-dimensional nilpotent spaces, or finite-dimensional spaces respectively ([4], theorem D, theorem A). The theory of localization for nilpotent groups has been developed by several authors (see [8]). The aim of this paper is to prove the following theorem. The corresponding result for E#(X) is obtained in [9], theorem 0·1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 2 , September 1990 , pp. 291 - 297
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

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