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

2011/11/18 by Urtzi Buijs, Buijs, Urtzi, Samuel B. Smith +1
Mathematics · #55P15 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:55P15

paper · pdf · doi:10.48550/arxiv.1111.4404

15 pages

arxiv created 2011/11/18 · arxiv updated 2011/11/21

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.

Related

• The rational homotopy type of the space of self-equivalences of a fibration
• Rational models for automorphisms of fiber bundles
• Lie models of homotopy automorphism monoids and classifying fibrations
• Algebraic models for classifying spaces of fibrations
• Realizing spaces as classifying spaces