Algebra/Topology seminar

Speaker: Robin Stoll

Title: The stable cohomology of block diffeomorphisms of connected sums of S^k × S^l

Abstract:
I will explain an identification of the stable rational cohomology of the classifying spaces of self-equivalences as well as block
diffeomorphisms of connected sums of S^k × S^l (relative to an embedded disk), where 2 < k < l < 2k–1. The result is expressed in terms of versions of Lie graph complex homology, the constructions of which I
will recall.
This also leads to a computation, in a range of degrees, of the stable rational cohomology of the classifying spaces of diffeomorphisms of these manifolds. In the case l = k+1, this recovers and extends recent results of Ebert-Reinhold.
If time permits, I will explain parts of the proof; this includes in particular work joint with Berglund on a certain type of algebraic
models for relative self-equivalences, inspired by results of Berglund-Zeman.