A \(K\)-theoretic relative index theorem and Callias-type Dirac operators

DOI10.1007/BF01460989zbMath0835.58035MaRDI QIDQ1907190

Ulrich Bunke

Publication date: 21 April 1996

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165367

zbMATH Keywords

Dirac operators\(K\)-theoryrelative index theorem\(K\)-homologyCallias type operators

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) (Semi-) Fredholm operators; index theories (47A53) Exotic index theories on manifolds (58J22) Global Riemannian geometry, including pinching (53C20) Ext and (K)-homology (19K33) Index theory (19K56)

Related Items (56)

Relative index theorem in \(K\)-homology ⋮ Higher genera for proper actions of Lie groups. II: The case of manifolds with boundary ⋮ SPECTRAL FLOW, INDEX AND THE SIGNATURE OPERATOR ⋮ Equivariant Callias index theory via coarse geometry ⋮ The Spectral Shift Function and the Witten Index ⋮ An equivariant index for proper actions. I ⋮ Dimension of monopoles on asymptotically conic 3-manifolds: Figure 1. ⋮ Index of equivariant Callias-type operators and invariant metrics of positive scalar curvature ⋮ Rho-classes, index theory and Stolz’ positive scalar curvature sequence ⋮ Infinite loop spaces and positive scalar curvature ⋮ Positive scalar curvature on simply connected spin pseudomanifolds ⋮ On a \(KK\)-theoretic counterpart of relative index theorems ⋮ The index of Callias-type operators with Atiyah-Patodi-Singer boundary conditions ⋮ Quantization of Hamiltonian loop group spaces ⋮ Spectral asymmetry and index theory on manifolds with generalised hyperbolic cusps ⋮ Callias-type operators associated to spectral triples ⋮ A quantitative relative index theorem and Gromov's conjectures on positive scalar curvature (with an appendix by Jinmin Wang and Zhizhang Xie) ⋮ A geometric approach to $K$-homology for Lie manifolds ⋮ Approximations of delocalized eta invariants by their finite analogues ⋮ Relative equivariant coarse index and relative \(L^2\)-index ⋮ On the space of initial values strictly satisfying the dominant energy condition ⋮ A geometric realisation of tempered representations restricted to maximal compact subgroups ⋮ Mapping the surgery exact sequence for topological manifolds to analysis ⋮ A relative higher index theorem, diffeomorphisms and positive scalar curvature ⋮ A long neck principle for Riemannian spin manifolds with positive scalar curvature ⋮ Callias-type operators in C∗-algebras and positive scalar curvature on noncompact manifolds ⋮ Width, largeness and index theory ⋮ An index formula for perturbed Dirac operators on Lie manifolds ⋮ A \(KK\)-theoretic perspective on deformed Dirac operators ⋮ Higher invariants in noncommutative geometry ⋮ Positive scalar curvature and an equivariant Callias-type index theorem for proper actions ⋮ Callias-type operators in von Neumann algebras ⋮ Higher rho invariants and the moduli space of positive scalar curvature metrics ⋮ A fixed point theorem on noncompact manifolds ⋮ Spectral theory of von Neumann algebra valued differential operators over non-compact manifolds ⋮ Positive scalar curvature on spin pseudomanifolds: the fundamental group and secondary invariants ⋮ A short proof of an index theorem ⋮ Positive scalar curvature, higher rho invariants and localization algebras ⋮ Orbifold index and equivariant \(K\)-homology ⋮ Infinite loop spaces and positive scalar curvature in the presence of a fundamental group ⋮ The Atiyah-Patodi-Singer index on manifolds with non-compact boundary ⋮ Product formula for Atiyah-Patodi-Singer index classes and higher signatures ⋮ Cauchy data spaces and Atiyah-Patodi-Singer index on non-compact manifolds ⋮ Index theory for locally compact noncommutative geometries ⋮ The index of a local boundary value problem for strongly Callias-type operators ⋮ KO-HOMOLOGY AND TYPE I STRING THEORY ⋮ An index theorem of Callias type for pseudodifferential operators ⋮ Two-cocycle twists and Atiyah–Patodi–Singer index theory ⋮ Spectral flows of Toeplitz operators and bulk-edge correspondence ⋮ A Callias-Type Index Theorem with Degenerate Potentials ⋮ Higher localised \(\hat{A}\)-genera for proper actions and applications ⋮ Coarse geometry and Callias quantisation ⋮ The relative index theorem for general first-order elliptic operators ⋮ Band width estimates via the Dirac operator ⋮ Invertible Dirac operators and handle attachments on manifolds with boundary ⋮ On the topological contents of \(\eta\)-invariants

Cites Work

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