Delocalized eta invariants, cyclic cohomology and higher rho invariants

DOI10.2140/akt.2023.8.531arXiv1901.02378OpenAlexW2909877296MaRDI QIDQ6066220

Jin-Min Wang, Xiaoman Chen, Zhizhang Xie, Guo-Liang Yu

Publication date: 12 December 2023

Published in: Annals of \(K\)-Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.02378

zbMATH Keywords

cyclic cohomologyhigher eta invariantshigher indexhigher rho invariantsConnes-Chern charactershigher index theorem for manifolds with boundaryhigher secondary invariants

Mathematics Subject Classification ID

(K)-theory and homology; cyclic homology and cohomology (19D55) Index theory (19K56)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on the higher Atiyah-Patodi-Singer index theorem on Galois coverings
• Realizing the analytic surgery group of Higson and Roe geometrically. III: Higher invariants
• The Atiyah-Patodi-Singer index theorem for Dirac operators over \(C^*\)-algebras
• Higher rho invariants and the moduli space of positive scalar curvature metrics
• Group cohomology and the cyclic cohomology of crossed products
• The Baum-Connes conjecture with coefficients for hyperbolic groups
• On the Chern character of \(\theta \) summable Fredholm modules
• Groups with torsion, bordism and rho invariants
• New holomorphically closed subalgebras of \(C^*\)-algebras of hyperbolic groups
• Superconnections and the Chern character
• Non-commutative differential geometry
• The cyclic homology of the group rings
• A short proof of the local Atiyah-Singer index theorem
• Quantum K-theory. I: The Chern character
• Entire cyclic cohomology of Banach algebras and characters of \(\theta\)- summable Fredholm modules
• Higher eta-invariants
• Geometric \(K\)-homology and controlled paths
• Localization algebras and the coarse Baum-Connes conjecture
• Bivariant \(K\)-theory for Banach algebras and the Baum-Connes conjecture
• The Baum-Connes conjecture for hyperbolic groups.
• Bounds on the von Neumann dimension of \(L^ 2\)-cohomoloy and the Gauss- Bonnet theorem for open manifolds
• Delocalized \(L^2\)-invariants
• Positive scalar curvature, higher rho invariants and localization algebras
• Mapping surgery to analysis. III: Exact sequences
• Mapping surgery to analysis. II: Geometric signatures
• Mapping surgery to analysis. I: Analytic signatures
• Secondary higher invariants and cyclic cohomology for groups of polynomial growth
• Positive scalar curvature and product formulas for secondary index invariants
• Rho-classes, index theory and Stolz’ positive scalar curvature sequence
• COMBABLE GROUPS HAVE GROUP COHOMOLOGY OF POLYNOMIAL GROWTH
• Rapidly Decreasing Functions in Reduced C ∗ -Algebras of Groups
• η-Invariants and Their Adiabatic Limits
• The $b$-pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem
• Homotopy invariance of twisted higher signatures on manifolds with boundary
• Additivity of Higher Rho Invariants and Nonrigidity of Topological Manifolds
• Delocalized Eta Invariants, Algebraicity, and K-Theory of Group C*-Algebras
• Coarse cohomology and index theory on complete Riemannian manifolds
• Straightening and bounded cohomology of hyperbolic groups

This page was built for publication: Delocalized eta invariants, cyclic cohomology and higher rho invariants