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Rational homotopy theory of automorphisms of highly connected manifolds

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Grothendieck-Teichmller Groups, Deformation and Operads

I will talk about joint work with Ib Madsen on the rational homotopy type of classifying spaces of various kinds of automorphisms of highly connected manifolds. The cohomology of the classifying space of the automorphisms of a g-fold connected sum of Sd x Sd stabilizes degreewise as g tends to infinity. For diffeomorphisms, the stable cohomology has been calculated by Galatius and Randal-Williams. I will discuss recent results on the stable cohomology for homotopy equivalences and for block diffeomorphisms. Curiously, the calculation in these cases involves certain Lie algebras of symplectic derivations that have appeared before in Kontsevich’s work on the cohomology of outer automorphisms of free groups.

This talk is part of the Isaac Newton Institute Seminar Series series.

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