Nonunital spectral triples and metric completeness in unbounded \(KK\)-theory

DOI10.1016/j.jfa.2016.08.004zbMath1345.19003arXiv1502.04520OpenAlexW2115804341MaRDI QIDQ313987

Bram Mesland, Adam Rennie

Publication date: 12 September 2016

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.04520

zbMATH Keywords

operator algebra\(KK\)-theoryapproximate unitunbounded Kasparov module

Mathematics Subject Classification ID

Complete metric spaces (54E50) (K)-theory and operator algebras (including cyclic theory) (46L80) Operator spaces and completely bounded maps (46L07) General theory of (C^*)-algebras (46L05) Kasparov theory ((KK)-theory) (19K35)

Related Items (25)

Schatten classes for Hilbert modules over commutative \(C^\ast \)-algebras ⋮ Curvature of differentiable Hilbert modules and Kasparov modules ⋮ The Kasparov product on submersions of open manifolds ⋮ Chern numbers, localisation and the bulk-edge correspondence for continuous models of topological phases ⋮ Sums of regular self-adjoint operators in Hilbert-\(C^{\ast}\)-modules ⋮ Equivariant \(KK\)-theory for non-Hausdorff groupoids ⋮ Noncommutative geometry for symmetric non-self-adjoint operators ⋮ Index theory and topological phases of aperiodic lattices ⋮ Homotopy equivalence in unbounded \(KK\)-theory ⋮ From Monge to Higgs: a survey of distance computations in noncommutative geometry ⋮ Riemannian submersions and factorization of Dirac operators ⋮ On the unbounded picture of \(KK\)-theory ⋮ Locally bounded perturbations and (odd) unbounded $KK$-theory ⋮ Poincaré duality for Cuntz-Pimsner algebras ⋮ Gauge theory on noncommutative Riemannian principal bundles ⋮ The \(K\)-theoretic bulk-edge correspondence for topological insulators ⋮ On the global limiting absorption principle for massless Dirac operators ⋮ A non-commutative framework for topological insulators ⋮ Wieler solenoids, Cuntz–Pimsner algebras and -theory ⋮ FACTORISATION OF EQUIVARIANT SPECTRAL TRIPLES IN UNBOUNDED -THEORY ⋮ Lifting spectral triples to noncommutative principal bundles ⋮ The unbounded Kasparov product by a differentiable module ⋮ Dynamics of compact quantum metric spaces ⋮ Immersions and the unbounded Kasparov product: embedding spheres into Euclidean space ⋮ Hecke operators in \(KK\)-theory and the \(K\)-homology of Bianchi groups

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