Analytic and topological index maps with values in the \(K\)-theory of mapping cones

DOI10.4171/JNCG/245zbMath1362.58009arXiv1302.4296MaRDI QIDQ740105

Robin J. Deeley

Publication date: 12 August 2016

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.4296

zbMATH Keywords

index theory\(K\)-homologymapping coneshigher Atiyah-Patodi-Singer index theory

Mathematics Subject Classification ID

(K)-theory and operator algebras (including cyclic theory) (46L80) Exotic index theories on manifolds (58J22) Ext and (K)-homology (19K33) Kasparov theory ((KK)-theory) (19K35)

Related Items (2)

Realizing the analytic surgery group of Higson and Roe geometrically. II: Relative \(\eta\)-invariants ⋮ The relative Mishchenko-Fomenko higher index and almost flat bundles. I: The relative Mishchenko-Fomenko index

Cites Work

• \(K\)-homology, assembly and rigidity theorems for relative eta invariants
• The Baum-Connes conjecture via localisation of categories
• Bordism, rho-invariants and the Baum-Connes conjecture
• Equivariant KK-theory and the Novikov conjecture
• \({\mathbb{Z}}/k\)-manifolds and families of Dirac operators
• A mod \(k\) index theorem
• Families of Dirac operators, boundaries and the \(B\)-calculus
• Dirac index classes and the noncommutative spectral flow
• Bivariant K-theory via correspondences
• \(L^2\)-index theorems, KK-theory, and connections
• Product formula for Atiyah-Patodi-Singer index classes and higher signatures
• R/Z-valued index theory via geometric K-homology
• Index theory, bordism, and 𝐾-homology

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