Abstract
Let be a closed –dimensional spin manifold which admits a metric of positive scalar curvature and let be the space of all such metrics. For any , Hitchin used the –valued –invariant to define a homomorphism . He then showed that if or and that if or .
In this paper we use Hitchin’s methods and extend these results by proving that
whenever and . The new input are elements with nontrivial –invariant deep down in the Gromoll filtration of the group . We show that for . This information about elements existing deep in the Gromoll filtration is the second main new result of this note.
Citation
Diarmuid Crowley. Thomas Schick. "The Gromoll filtration, $\mathit{KO}$–characteristic classes and metrics of positive scalar curvature." Geom. Topol. 17 (3) 1773 - 1789, 2013. https://doi.org/10.2140/gt.2013.17.1773
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