Bernhard Hanke, Thomas Schick, Wolfgang Steimle
Published 2012-12-01, updated 2014-02-12Version 3
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 of infinite order 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-hat-genera, thus establishing the non-multiplicativity of the A-hat-genus in fibre bundles with simply connected base.
Comments: 24 pages, v2: minor additions and corrections, based in particular on comments of referees, v3: minor corrections, final version, to appear in Publ.Math. IHES
On moduli spaces of positive scalar curvature metrics on certain manifolds
A quasifibration of spaces of positive scalar curvature metrics
A plug with infinite order and some exotic 4-manifolds
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