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Rational homotopy theory of automorphisms of highly connected manifolds

Presented by: 
A Berglund Stockholm University
Tuesday 2nd April 2013 - 13:30 to 14:30
INI Seminar Room 1
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 S^d x S^d 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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons