The rational homotopy type of the space of self-equivalences of a fibration

Yves Felix; Gregory Lupton; Samuel B. Smith

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arXiv · 0903.1470

The rational homotopy type of the space of self-equivalences of a fibration

Yves Felix·Gregory Lupton·Samuel B. Smith

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Abstract

Let Aut(p) denote the topological monoid of self-fibre-homotopy equivalences of a fibration p:E\to B. We make a general study of this monoid, especially in rational homotopy theory. When E and B are simply connected CW complexes with E finite, we identify the rational Samelson Lie algebra of the identity component of Aut(p) as the homology of a certain DG Lie algebra of derivations arising from the Koszul-Sullivan model of p. We obtain related identifications for the rational homotopy groups of fibrewise mapping spaces and for the rationalization of a natural nilpotent subgroup of Aut(p).

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Yves Felix, Gregory Lupton, Samuel B. Smith. 2010-09-04. The rational homotopy type of the space of self-equivalences of a fibration. https://arxiv.org/abs/0903.1470

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