Callias-type operators associated to spectral triples

DOI10.4171/jncg/505zbMath1527.46047arXiv2108.06368OpenAlexW3195019507MaRDI QIDQ6111632

Tom Stoiber, Hermann Schulz-Baldes

Publication date: 4 August 2023

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

Full work available at URL: https://arxiv.org/abs/2108.06368

zbMATH Keywords

spectral flowindex theoremCallias operator

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) (K)-theory and operator algebras (including cyclic theory) (46L80) Noncommutative geometry (à la Connes) (58B34) Index theory (19K56)

Related Items

Spectral localization for semimetals and Callias operators ⋮ Spectral localizer for line-gapped non-Hermitian systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bulk and boundary invariants for complex topological insulators. From \(K\)-theory to physics
• The Callias index formula revisited
• A local global principle for regular operators in Hilbert \(C^*\)-modules
• Spectral flow is the integral of one forms on the Banach manifold of self adjoint Fredholm operators
• The joint spectral flow and localization of the indices of elliptic operators
• Axial anomalies and index theorems on open spaces
• The spectral localizer for even index pairings
• Cycles and relative cycles in analytic K-homology
• Unbounded elements affiliated with \(C^*\)-algebras and non-compact quantum groups
• On the index of Toeplitz operators of several complex variables
• Some remarks on the paper of Callias
• An index theorem for Toeplitz operators with noncommutative symbol space
• \(K\)-homology and regular singular Dirac-Schrödinger operators on even-dimensional manifolds
• Ordinary differential operators in Hilbert spaces and Fredholm pairs
• Callias-type operators in von Neumann algebras
• A \(K\)-theoretic relative index theorem and Callias-type Dirac operators
• Homotopy equivalence in unbounded \(KK\)-theory
• On the unbounded picture of \(KK\)-theory
• The index of generalised Dirac-Schrödinger operators
• Spectral flow of monopole insertion in topological insulators
• Boundaries, spectral triples and \(K\)-homology
• Finite volume calculation of \(K\)-theory invariants
• Sums of regular self-adjoint operators in Hilbert-\(C^{\ast}\)-modules
• Spectral flow and the unbounded Kasparov product
• The local index formula in semifinite von Neumann algebras. I: Spectral flow
• The local index formula in semifinite von Neumann algebras. II: the even case
• Index theory for locally compact noncommutative geometries
• Quantization of interface currents
• SPECTRAL INVARIANCE OF DENSE SUBALGEBRAS OF OPERATOR ALGEBRAS
• KK-Theory and Spectral Flow in von Neumann Algebras
• SPECTRAL FLOW AND WINDING NUMBER IN VON NEUMANN ALGEBRAS
• On crossed products and Takai duality
• Unbounded Fredholm Modules and Spectral Flow
• Unbounded Fredholm Operators and Spectral Flow
• A NOTE ON TOEPLITZ OPERATORS
• The Spectral Flow and the Maslov Index
• The Cayley transform in complex, real and graded K-theory
• Callias-type operators in C∗-algebras and positive scalar curvature on noncompact manifolds
• The spectral localizer for semifinite spectral triples
• Spectral Flow for Nonunital Spectral Triples