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self-homotopy equivalences

Proceedings of the Edinburgh Mathematical Society (1)

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ON THE GROUP AutΩ(X)
Petar Paves˘ić
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Proceedings of the Edinburgh Mathematical Society / Volume 45 / Issue 3 / October 2002

Published online by Cambridge University Press:

14 October 2002, pp. 673-680
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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