Rational Homotopy Type of the Classifying Space for Fibrewise Self-Equivalences
Abstract
Let p be a fibration of simply connected CW complexes with finite base B and fibre F. Let aut1(p) denote the identity component of the space of all fibre-homotopy self-equivalences of p and Baut1(p) the classifying space for this topological monoid. We give a differential graded Lie algebra model for Baut1(p). We use this model to give classification results for the rational homotopy types represented by Baut1(p) and also to obtain conditions under which the monoid aut1(p) is a double loop-space after rationalization.
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