Algebra/Topology seminar

Speaker: Diarmuid Crowley 

Title: The Gromoll filtration, Toda brackets and positive scalar curvature'

Abstract: 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 fibred over the projection D^n \to D^{n-k}.In this talk I will present a new method for constructing exotic spheres with small disc of origin via Toda brackets in the space PL_k/O_k and a theorem of Morlet. 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 these results for the space of positive scalar curvature metrics on spin manifolds of dimension 6 and higher.