Harmonic spinors and metrics of positive curvature via the Gromoll filtration and Toda brackets

Diarmuid Crowley, Thomas Schick, Wolfgang Steimle

We construct non-trivial elements of order 2 in the homotopy groups ${\pi }_{8j+1+\ast }Diff(D^6,\partial )$, for * congruent 1 or 2 modulo 8, which are detected by the "assembling homomorp…