The space of metrics of positive scalar curvature

Hanke, Bernhard; Schick, Thomas; Steimle, Wolfgang

Publications Mathématiques de l'IHÉS, Tome 120 (2014), pp. 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 $\widehat{A}$-genera, thus establishing the non-multiplicativity of the $\widehat{A}$-genus in fiber bundles with simply connected base.

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