The space of metrics of positive scalar curvature

@article{Hanke2014TheSO,
  title={The space of metrics of positive scalar curvature},
  author={Bernhard Hanke and Thomas Schick and Wolfgang Steimle},
  journal={Publications math{\'e}matiques de l'IH{\'E}S},
  year={2014},
  volume={120},
  pages={335-367}
}
We study the topology of the space of positive scalar curvature metrics on high dimensional spheres and other spin manifolds. Our main result provides elements in higher homotopy and homology groups of these spaces, which, in contrast to previous approaches, are of infinite order and survive in the (observer) moduli space of such metrics.Along the way we construct smooth fiber bundles over spheres whose total spaces have non-vanishing $\hat{A}$-genera, thus establishing the non-multiplicativity… 

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