The space of metrics of positive scalar curvature

Abstract

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.

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

References in corpus (1)

• The Gromoll filtration, KO-characteristic classes and metrics of positive scalar curvature

Cited by in corpus (15)

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• Homotopy groups of the observer moduli space of Ricci positive metrics
• On the topology of moduli spaces of non-negatively curved Riemannian metrics
• Bundles with non-multiplicative $\hat{A}$-genus and spaces of metrics with lower curvature bounds
• Metrics with non-negative Ricci curvature on convex three-manifolds
• Non-negative versus positive scalar curvature
• On moduli spaces of positive scalar curvature metrics on highly connected manifolds
• On the space of initial values strictly satisfying the dominant energy condition
• Moduli spaces of invariant metrics of positive scalar curvature on quasitoric manifolds
• Some rational homology computations for diffeomorphisms of odd-dimensional manifolds
• Positive $(p,n)$-intermediate scalar curvature and cobordism
• Spaces of Positive Scalar Curvature metrics on totally nonspin Manifolds with spin boundary