Fibred coarse embedding into non-positively curved manifolds and higher index problem

DOI10.1016/j.jfa.2014.10.004zbMath1306.53029OpenAlexW2083478625MaRDI QIDQ466233

Xiaoman Chen, Qin Wang, Zhijie Wang

Publication date: 24 October 2014

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2014.10.004

zbMATH Keywords

K-theorycoarse geometrycoarse Novikov conjecturenon-positively curved manifoldsRips complexRoe algebra

Mathematics Subject Classification ID

Characteristic classes and numbers in differential topology (57R20) Global Riemannian geometry, including pinching (53C20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)

Related Items

\(K\)-theory of relative group \(C^*\)-algebras and the relative Novikov conjecture ⋮ Group approximation in Cayley topology and coarse geometry Part I: Coarse embeddings of amenable groups ⋮ Group approximation in Cayley topology and coarse geometry. II: Fibred coarse embeddings

Cites Work

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• A concentration theorem of expanders on Hadamard manifolds
• Higher index theory for certain expanders and Gromov monster groups. I
• Higher index theory for certain expanders and Gromov monster groups. II
• The coarse geometric Novikov conjecture and uniform convexity
• K-theory for the maximal Roe algebra of certain expanders
• Equivariant KK-theory and the Novikov conjecture
• The Novikov conjecture for groups with finite asymptotic dimension
• Discrete groups, expanding graphs and invariant measures. Appendix by Jonathan D. Rogawski
• Localization algebras and the coarse Baum-Connes conjecture
• Groups acting properly on ``bolic spaces and the Novikov conjecture
• Geometric \(K\)-theory for Lie groups and foliations
• Coarse Baum-Connes conjecture
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• The coarse geometric Novikov conjecture for subspaces of non-positively curved manifolds
• The maximal coarse Baum-Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space
• Characterization of the Haagerup property by fibred coarse embedding into Hilbert space
• A coarse Mayer–Vietoris principle
• Localization Algebras and Duality
• Geometrization of the Strong Novikov Conjecture for residually finite groups
• TOPOLOGICAL INVARIANTS OF ELLIPTIC OPERATORS. I:K-HOMOLOGY
• Operator 𝐾-theory for groups which act properly and isometrically on Hilbert space
• Maximal and reduced Roe algebras of coarsely embeddable spaces
• Coarse cohomology and index theory on complete Riemannian manifolds
• BOTT PERIODICITY AND THE INDEX OF ELLIPTIC OPERATORS
• \(E\)-theory and \(KK\)-theory for groups which act properly and isometrically on Hilbert space