Metrics with positive scalar curvature at infinity and localization algebra

DOI10.1007/s11401-021-0252-yzbMath1479.19006OpenAlexW3150303886WikidataQ114222476 ScholiaQ114222476MaRDI QIDQ2044105

Hongzhi Liu, Xiao-Fei Zhang, Yanlin Liu

Publication date: 4 August 2021

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-021-0252-y

zbMATH Keywords

higher index theory\(K\)-theory of \(C^*\)-algebraspositive scalar curvature at infinity

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Spin and Spin({}^c) geometry (53C27) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Index theory (19K56)

Cites Work

• Positive scalar curvature and the Dirac operator on complete Riemannian manifolds
• The Novikov conjecture for groups with finite asymptotic dimension
• Spin and scalar curvature in the presence of a fundamental group. I
• Localization algebras and the coarse Baum-Connes conjecture
• Arithmetic manifolds of positive scalar curvature
• Positive scalar curvature, higher rho invariants and localization algebras
• A relative higher index theorem, diffeomorphisms and positive scalar curvature
• Higher Index Theory
• Coarse cohomology and index theory on complete Riemannian manifolds
• The index of elliptic operators on compact manifolds
• Positive Curvature, Partial Vanishing Theorems and Coarse Indices
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