Revistes Catalanes amb Accés Obert (RACO)

Nilpotent subgroups of the group of fibre homotopy equivalences

Y. Félix, J. C. Thomas


Let $\xi=(E,p,B,F)$ be a Hurewicz fibration. In this paper we study the space $\Cal L_G(\xi)$ consisting of fibre homotopy self equivalences of $\xi$ inducing by restriction to the fibre a self homotopy equivalence of $F$ belonging to the group $G$. We give in particular conditions implying that $\pi_1(\Cal L_G(\xi))$ is finitely generated or that $\Cal L_1(\xi)$ has the same rational homotopy type as $\operatorname{aut}_1(F)$.

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