The Gromoll filtration, KO–characteristic classes and metrics of positive scalar curvature

@inproceedings{Crowley2013TheGF,
  title={The Gromoll filtration, KO–characteristic classes and metrics of positive scalar curvature},
  author={Diarmuid J. Crowley and Thomas Schick},
  year={2013}
}
  • Diarmuid J. Crowley, Thomas Schick
  • Published 2013
  • Mathematics
  • Let X be a closed m-dimensional spin manifold which admits a metric of positive scalar curvature and let Pos(X) be the space of all such metrics. For any g in Pos(X), Hitchin used the KO-valued alpha-invariant to define a homomorphism A_{n-1} from \pi_{n-1}(Pos(X) to KO_{m+n}. He then showed that A_0 is not 0 if m = 8k or 8k+1 and that A_1 is not 0 if m = 8k-1 or 8$. In this paper we use Hitchin's methods and extend these results by proving that A_{8j+1-m} is not 0 whenever m>6 and 8j - m… CONTINUE READING

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