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ON THE GROUP AutΩ(X)

Published online by Cambridge University Press:  14 October 2002

Petar Paves˘ić
Petar Paves˘ić
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19, Ljubljana, Slovenia (petar.pavesic@uni-lj.si)
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Abstract

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Felix and Murillo introduced the group $\mathrm{Aut}_\varOmega(X)$ of self-maps $f$ of $X$, which satisfy $\sOm f=1_{\varOmega X}$, and proved that the group is nilpotent with the order of nilpotency bounded by the Lusternik–Schnirelmann category of $X$. In this paper we construct a spectral sequence converging to the group $\mathrm{Aut}_\varOmega(X)$ and derive several interesting consequences.

AMS 2000 Mathematics subject classification: Primary 55P42

Keywords

self-homotopy equivalencesloop spacesspectral sequences
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 3 , October 2002 , pp. 673 - 680
Copyright
Copyright © Edinburgh Mathematical Society 2002