The derivative map for diffeomorphisms of discs: an example

Diarmuid Crowley, University of Melbourne

Online Talk 

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Passcode: 998749

Taking the derivative of a diffeomorphism of a k-disc, which is the identity near the boundary, defines the derivative map d^k : Diff(D^k) \to \Omega^k(SO_k). In this talk I will explain how a recent result of Burklund and Senger about a certain exotic 17-sphere can be used to show that the map induced by d^11 is non-zero on \pi_5. Via smoothing theory, the result above corresponds to the statement that there is a non-trivial rank 11 vector bundle of the 17-sphere, which becomes trivial as a topological R^11-bundle.  This is the first known example of such a vector bundle.

This is part of joint work with Thomas Schick and Wolfgang Steimle: arXiv:2012.13634