Rational Homotopy Type of the Classifying Space for Fibrewise Self-Equivalences

Urtzi Buijs; Samuel B. Smith

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arXiv · 1111.4404

Rational Homotopy Type of the Classifying Space for Fibrewise Self-Equivalences

Urtzi Buijs·Samuel B. Smith

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Abstract

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.

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BibTeX RIS

Urtzi Buijs, Samuel B. Smith. 2011-11-18. Rational Homotopy Type of the Classifying Space for Fibrewise Self-Equivalences. https://arxiv.org/abs/1111.4404

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