Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T15:38:45.746Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)