Rational Homotopy Type of the Classifying Space for Fibrewise   Self-Equivalences
  Let p be a fibration of simply connected CW complexes with finite base B and fibre F. Let aut_1(p) denote the identity component of the space of all fibre-homotopy self-equivalences of p and Baut_1(p) the classifying space for this topological monoid. We give a differential graded Lie algebra model for Baut_1(p). We use this model to give classification results for the rational homotopy types represented by Baut_1(p) and also to obtain conditions under which the monoid aut_1(p) is a double loop-space after rationalization. 
Urtzi Buijs and Samuel B. Smith
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