A relative higher index theorem, diffeomorphisms and positive scalar curvature

DOI10.1016/j.aim.2013.09.011zbMath1306.58006arXiv1204.3664OpenAlexW2963921401MaRDI QIDQ2445374

Zhizhang Xie, Guo-Liang Yu

Publication date: 14 April 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.3664

zbMATH Keywords

\(K\)-theorypositive scalar curvaturehigher index theorygroup \(C^*\)-algebras

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Index theory and related fixed-point theorems on manifolds (58J20) Spin and Spin({}^c) geometry (53C27)

Related Items (17)

Finite part of operator \(K\)-theory for groups finitely embeddable into Hilbert space and the degree of nonrigidity of manifolds ⋮ A quantitative relative index theorem and Gromov's conjectures on positive scalar curvature (with an appendix by Jinmin Wang and Zhizhang Xie) ⋮ Approximations of delocalized eta invariants by their finite analogues ⋮ Relative equivariant coarse index and relative \(L^2\)-index ⋮ Property RD and the classification of traces on reduced group C∗-algebras of hyperbolic groups ⋮ Codimension 2 transfer of higher index invariants ⋮ Higher invariants in noncommutative geometry ⋮ The relative \(L^2\) index theorem for Galois coverings ⋮ Higher rho invariants and the moduli space of positive scalar curvature metrics ⋮ Positive scalar curvature on spin pseudomanifolds: the fundamental group and secondary invariants ⋮ Positive scalar curvature, higher rho invariants and localization algebras ⋮ The Higson-Roe exact sequence and \(\ell^2\) eta invariants ⋮ The relative Mishchenko-Fomenko higher index and almost flat bundles. I: The relative Mishchenko-Fomenko index ⋮ Metrics with positive scalar curvature at infinity and localization algebra ⋮ Positive scalar curvature and a new index theory for noncompact manifolds ⋮ Positive scalar curvature and product formulas for secondary index invariants ⋮ Strong Novikov conjecture for low degree cohomology and exotic group C*-algebras

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• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• The index of elliptic operators. IV, V
• On the Baum-Connes conjecture in the real case
• The index of elliptic operators on compact manifolds

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