RATIONAL HOMOTOPY TYPE OF THE CLASSIFYING SPACE FOR FIBREWISE SELF-EQUIVALENCES.

Let p: E . B 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. Let Baut1 (p) denote the classifying space for this topological monoid. We give a differential graded Lie algebra model for Baut1(p), connecting the results of recent work by the authors and others. We use this model to give classification results for the rational homotopy types represented by Baut11(p) and also to obtain conditions under which the monoid aut11(p) is a double loop-space after rationalization. [ABSTRACT FROM AUTHOR]