Nonconnected moduli spaces of nonnegative sectional curvature metrics on simply connected manifolds

DOI10.1112/blms.12095zbMath1385.53022arXiv1601.04877OpenAlexW3123148434WikidataQ125975276 ScholiaQ125975276MaRDI QIDQ4604598

Stephan Klaus, Anand Dessai, Wilderich Tuschmann

Publication date: 2 March 2018

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.04877

zbMATH Keywords

group of diffeomorphismsspace of Riemannian metricsnonnegative sectional curvatureKreck-Stolz s-invariantmoduli space of Riemannian metrics

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Moduli problems for differential geometric structures (58D27) Global Riemannian geometry, including pinching (53C20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Differentiable structures in differential topology (57R55) Algebraic topology on manifolds and differential topology (57R19) Manifolds of metrics (especially Riemannian) (58D17)

Related Items (11)

Moduli space of nonnegatively curved metrics on manifolds of dimension \(4k+1\) ⋮ Diffeomorphic souls and disconnected moduli spaces of nonnegatively curved metrics ⋮ Moduli space of non-negative sectional or positive Ricci curvature metrics on sphere bundles over spheres and their quotients ⋮ Infinite families of manifolds of positive \(k\)th-intermediate Ricci curvature with \(k\) small ⋮ Non-negative versus positive scalar curvature ⋮ Moduli space of metrics of nonnegative sectional or positive Ricci curvature on homotopy real projective spaces ⋮ Homotopy groups of the observer moduli space of Ricci positive metrics ⋮ On the moduli spaces of metrics with nonnegative sectional curvature ⋮ On the topology of moduli spaces of non-negatively curved Riemannian metrics ⋮ The moduli space of nonnegatively curved metrics on quotients of \(S^2 \times S^3\) by involutions ⋮ Index theory and deformations of open nonnegatively curved manifolds

Cites Work

• The Gromoll filtration, \(KO\)-characteristic classes and metrics of positive scalar curvature
• Moduli spaces of nonnegative sectional curvature and non-unique souls
• Deforming three-manifolds with positive scalar curvature
• \(H\)-spaces, loop spaces and the space of positive scalar curvature metrics on the sphere
• The space of metrics of positive scalar curvature
• Space of nonnegatively curved metrics and pseudoisotopies
• On the topology of the space of negatively curved metrics
• Einstein metrics on principal torus bundles
• On the moduli space of positive Ricci curvature metrics on homotopy spheres
• Homotopy groups of the moduli space of metrics of positive scalar curvature
• Riemannian metrics of positive scalar curvature on compact manifolds with boundary
• Infinitesimal computations in topology
• Harmonic spinors
• The eta invariant and metrics of positive scalar curvature
• The Teichmüller space of pinched negatively curved metrics on a hyperbolic manifold is not contractible
• Infinite loop spaces and positive scalar curvature
• Nonnegatively curved manifolds with finite fundamental groups admit metrics with positive Ricci curvature
• Non-negative pinching, moduli spaces and bundles with infinitely many souls
• Connectedness properties of the space of complete nonnegatively curved planes
• An invariant for certain smooth manifolds
• Cobordism invariance of the homotopy type of the space of positive scalar curvature metrics
• Metrics of positive scalar curvature and generalised Morse functions, part I
• Nonconnected Moduli Spaces of Positive Sectional Curvature Metrics
• Construction of Manifolds of Positive Scalar Curvature
• Spectral asymmetry and Riemannian Geometry. I
• Spectral asymmetry and Riemannian geometry. II
• The moduli space of negatively curved metrics of a hyperbolic manifold

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