The space of metrics of positive scalar curvature

Publications Mathématiques de l'Institut des Hautes Études Scientifiques - 2014
Bernhard Hanke1, Thomas Schick2, Wolfgang Steimle3
1Institut für Mathematik, Universität Augsburg, Augsburg, Germany
2Mathematisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany
3Mathematisches Institut, Universität Bonn, Bonn, Germany

Tóm tắt

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 of the $\hat{A}$ -genus in fiber bundles with simply connected base.

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