Rational homotopy theory of automorphisms of highly connected manifolds
(English)Manuscript (preprint) (Other academic)
We study the rational homotopy types of classifying spaces of automorphism groups of 2d-dimensional (d-1)-connected manifolds (d > 2). We prove that the rational homology groups of the homotopy automorphisms and the block diffeomorphisms of the manifold #^g S^d x S^d relative to a disk stabilize as g increases. Via a theorem of Kontsevich, we obtain the striking result that the stable rational cohomology of the homotopy automorphisms comprises all unstable rational homology groups of all outer automorphism groups of free groups.
Research subject Mathematics
IdentifiersURN: urn:nbn:se:su:diva-111897OAI: oai:DiVA.org:su-111897DiVA: diva2:777038