Speaker: Johannes Ebert
Title: On the rational homology of diffeomorphism groups for some odd-dimensional manifolds
Abstract: I'll talk about new results on the rational cohomology of the classifying space of the diffeomorphism group of the manifold Ung,1, which is the connected sum of g copies of Sn x Sn+1, minus a disc. This might be considered as an odd-dimensional analogue of Wng,1, the connected sum of g copies of Sn x Sn. The analogous problem for Wng,1 was solved in famous work by Madsen--Weiss (n=1) and Galatius--Randal-Williams (n geq 3), for large values of g.
For the manifolds Ung,1, we compute the rational cohomology for large g and in degrees up to n-4. The answer looks superficially similar in the sense that the cohomology is an exterior algebra in some generalized Miller--Morita--Mumford classes, with some notable differences.
The proof relies on the surgery-theoretic approach to automorphism groups of manifolds.
This is joint work with Jens Reinhold.