The derivative map for diffeomorphisms of discs: an example
The derivative map for diffeomorphisms of discs: an example

Diarmuid Crowley, University of Melbourne
Online Talk
Zoom link: https://princeton.zoom.us/j/96282936122
Passcode: 998749
Taking the derivative of a diffeomorphism of a kdisc, 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 17sphere can be used to show that the map induced by d^11 is nonzero on \pi_5. Via smoothing theory, the result above corresponds to the statement that there is a nontrivial rank 11 vector bundle of the 17sphere, which becomes trivial as a topological R^11bundle. 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