The Gromoll filtration, Toda brackets and positive scalar curvature

22 February 2016
OAC-manifolds meeting: Diarmuid Crowley
An exotic (n+1)-sphere has disc of origin D^k if k is the smallest integer such that some clutching diffeomorphism of the n-disc which builds the exotic sphere can be written as an (n-k)-parameter family of diffeomorphisms of the k-disc.
In this talk I will present a new method for constructing exotic spheres with small disc of origin via Toda brackets.  
This method gives exotic spheres in all dimensions 8j+1 and 8j+2 with disc of origin 6 and with Dirac operators of non-zero index (such spheres are often called "Hitchin spheres").
I will also briefly discuss implications of our results for the space of positive scalar curvature metrics on spin manifolds of dimension 6 and higher, and in particular the relationship of this project to the work of Botvinnik, Ebert and Randal-Williams.
This is part of joint work with Thomas Schick and Wolfgang Steimle.
  • Geometry and Analysis Seminar