The space of metrics of positive scalar curvature
Hanke, Bernhard1 ; Schick, Thomas2 ; Steimle, Wolfgang3
1 Institut für Mathematik, Universität Augsburg 86135 Augsburg Germany
2 Mathematisches Institut, Georg-August-Universität Göttingen 37073 Göttingen Germany
3 Mathematisches Institut, Universität Bonn 53115 Bonn Germany
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 A^-genera, thus establishing the non-multiplicativity of the A^-genus in fiber bundles with simply connected base.

DOI : 10.1007/s10240-014-0062-9
Mots-clés : Modulus Space, Normal Bundle, Homotopy Group, Spin Manifold, Positive Scalar Curvature
Hanke, Bernhard 1 ; Schick, Thomas 2 ; Steimle, Wolfgang 3

1 Institut für Mathematik, Universität Augsburg 86135 Augsburg Germany
2 Mathematisches Institut, Georg-August-Universität Göttingen 37073 Göttingen Germany
3 Mathematisches Institut, Universität Bonn 53115 Bonn Germany 
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     title = {The space of metrics of positive scalar curvature},
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Hanke, Bernhard; Schick, Thomas; Steimle, Wolfgang. The space of metrics of positive scalar curvature. Publications Mathématiques de l'IHÉS, Tome 120 (2014), pp. 335-367. doi : 10.1007/s10240-014-0062-9. https://www.numdam.org/articles/10.1007/s10240-014-0062-9/

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