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Moduli spaces of nonnegative sectional curvature and non-unique souls. (English) Zbl 1242.53035

J. Differ. Geom. 89, No. 1, 49-85 (2011); correction ibid. 119, No. 1, 183-185 (2021).
Authors’ abstract: We apply various topological methods to distinguish connected components of moduli spaces of complete Riemannian metrics of nonnegative sectional curvature on open manifolds. The new geometric ingredient is that souls of nearby nonnegatively curved metrics are ambiently isotopic.

MSC:

53C20 Global Riemannian geometry, including pinching
58D17 Manifolds of metrics (especially Riemannian)
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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