Detecting exotic smooth structures in diffeomorphism groups

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• Manuel Krannich, Cambridge
• Wednesday 14 November 2018, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

The well-studied inertia group of a closed manifold M captures the behaviour of the diffeomorphism type of M when changing the smooth structure of M on a codimension zero disc; that is, when taking the connected sum M#S with an exotic sphere S. Instead of comparing their diffeomorphism types, one might try to compare the group of diffeomorphisms of M and M#S. However, homotopically, the space of diffeomorphisms Diff(M) decomposes as a twisted product whose factors are insensitive to replacing M with M#S. This suggests that it is hard to detect the possible exotic nature of M#S by means of homotopical properties of its group of diffeomorphisms. Using recent progress in manifold theory by Galatius and Randal-Williams, together with computations in stable homotopy theory, I will discuss results on the behaviour of the cohomology of BDiff(M) when replacing M with M#S.

This talk is part of the Differential Geometry and Topology Seminar series.

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