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A NOTE ON THE NILPOTENCY OF SUBGROUPS OF SELF-HOMOTOPY EQUIVALENCES

Published online by Cambridge University Press:  01 July 1997

YVES FÉLIX  and
ANICETO MURILLO
YVES FÉLIX
Affiliation:
Institut Mathématique, Université Catholique de Louvain, 2 Chemin du cyclotron, 1348 Louvain-La-Neuve, Belgium
ANICETO MURILLO
Affiliation:
Departamento de Algebra, Geometria y Topologia, Universidad de Malaga, Campus Teatinos, Apartado 59, 29080 Malaga, Spain
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Abstract

Let X be a space that has the homotopy type of a finite simply connected CW complex. We denote by [Escr ](X) the group of homotopy classes of self-homotopy equivalences of X. This group has been extensively studied (see [1] for a survey). In this paper we consider the subgroup [Escr ]n#(X) consisting of homotopy classes of self-homotopy equivalences of X that induce the identity on the homotopy groups πi(X) for i[les ]n, and the subgroup [Escr ]#(X) consisting of homotopy classes of self-homotopy equivalences of X that induce the identity on all the homotopy groups. Our first result is as follows.

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 4 , July 1997 , pp. 486 - 488
Copyright
© The London Mathematical Society 1997

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