Rho-classes, index theory and Stolz’ positive scalar curvature sequence

DOI10.1112/jtopol/jtt048zbMath1320.58012arXiv1210.6892OpenAlexW3102892096MaRDI QIDQ2934807

Thomas Schick, Paolo Piazza

Publication date: 22 December 2014

Published in: Journal of Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.6892

zbMATH Keywords

Riemannian manifoldfundamental group\(K\)-theoryspin manifoldcoarse geometrypositive scalar curvature\(C^\ast\)-algebraindex theorem

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) (K)-theory and operator algebras (including cyclic theory) (46L80) Exotic index theories on manifolds (58J22) Spin and Spin({}^c) geometry (53C27) Index theory (19K56)

Related Items (33)

On the range of the relative higher index and the higher rho-invariant for positive scalar curvature ⋮ Higher genera for proper actions of Lie groups. II: The case of manifolds with boundary ⋮ An equivariant Atiyah-Patodi-Singer index theorem for proper actions. II: The \(K\)-theoretic index ⋮ Singular spaces, groupoids and metrics of positive scalar curvature ⋮ Spaces and moduli spaces of Riemannian metrics ⋮ Delocalized Eta Invariants, Algebraicity, and K-Theory of Group C*-Algebras ⋮ Realizing the analytic surgery group of Higson and Roe geometrically. III: Higher invariants ⋮ Higher \(\rho\) invariant is an obstruction to the inverse being local ⋮ Positive scalar curvature on simply connected spin pseudomanifolds ⋮ An equivariant PPV theorem and Paschke-Higson duality ⋮ Delocalized eta invariants, cyclic cohomology and higher rho invariants ⋮ Relative torsion and bordism classes of positive scalar curvature metrics on manifolds with boundary ⋮ Approximations of delocalized eta invariants by their finite analogues ⋮ Interior Kasparov products for \(\varrho\)-classes on Riemannian foliated bundles ⋮ Codimension 2 transfer of higher index invariants ⋮ Bounds on Cheeger-Gromov invariants and simplicial complexity of triangulated manifolds ⋮ Secondary higher invariants and cyclic cohomology for groups of polynomial growth ⋮ Mapping the surgery exact sequence for topological manifolds to analysis ⋮ Positive scalar curvature due to the cokernel of the classifying map ⋮ Higher invariants in noncommutative geometry ⋮ Adiabatic groupoid and secondary invariants in K-theory ⋮ 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 ⋮ Positive scalar curvature and low-degree group homology ⋮ Higher genera for proper actions of Lie groups ⋮ Additivity of higher rho invariant for the topological structure group from a differential point of view ⋮ Codimension two index obstructions to positive scalar curvature ⋮ Positive scalar curvature and product formulas for secondary index invariants ⋮ The adiabatic groupoid and the Higson-Roe exact sequence ⋮ Boundaries, spectral triples and \(K\)-homology ⋮ The Higson-Roe sequence for étale groupoids. I: Dual algebras and compatibility with the BC map ⋮ Slant products on the Higson-Roe exact sequence

Cites Work

• Unnamed Item
• Unnamed Item
• \(K\)-homology, assembly and rigidity theorems for relative eta invariants
• A note on the cobordism invariance of the index
• The surgery exact sequence, \(K\)-theory and the signature operator
• Bordism, rho-invariants and the Baum-Connes conjecture
• Index theory and partitioning by enlargeable hypersurfaces
• Higher eta-invariants
• Von Neumann index theorems for manifolds with boundary
• \(C^*\)-algebras and controlled topology
• On the homotopy invariance of higher signatures for manifolds with boundary
• On higher eta-invariants and metrics of positive scalar curvature
• Large scale index of multi-partitioned manifolds
• Cyclic cohomology, the Novikov conjecture and hyperbolic groups
• A \(K\)-theoretic relative index theorem and Callias-type Dirac operators
• The Godbillon-Vey cyclic cocycle and longitudinal Dirac operators
• Eta cocycles, relative pairings and the Godbillon-Vey index theorem
• Positive scalar curvature, higher rho invariants and localization algebras
• Superconnections and higher index theory
• Mapping surgery to analysis. III: Exact sequences
• Mapping surgery to analysis. II: Geometric signatures
• Mapping surgery to analysis. I: Analytic signatures
• \(L^2\)-index theorems, KK-theory, and connections
• A coarse Mayer–Vietoris principle
• Comparing Analytic Assembly Maps
• A NOTE ON THE RELATIVE INDEX THEOREM
• The $b$-pseudodifferential calculus on Galois coverings and a higher Atiyah-Patodi-Singer index theorem
• A Homotopy Invariance Theorem in Coarse Cohomology and K-Theory
• Homotopy invariance of twisted higher signatures on manifolds with boundary
• Higher ρ -invariants and the surgery structure set
• Codimension two index obstructions to positive scalar curvature

This page was built for publication: Rho-classes, index theory and Stolz’ positive scalar curvature sequence