Spectral flow and the unbounded Kasparov product
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Publication:2437530
DOI10.1016/j.aim.2013.08.015zbMath1294.19001arXiv1110.1472OpenAlexW2113241243MaRDI QIDQ2437530
Publication date: 3 March 2014
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1110.1472
(K)-theory and operator algebras (including cyclic theory) (46L80) Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Kasparov theory ((KK)-theory) (19K35) Spectral flows (58J30)
Related Items (36)
Gauge theory for spectral triples and the unbounded Kasparov product ⋮ Schatten classes for Hilbert modules over commutative \(C^\ast \)-algebras ⋮ Curvature of differentiable Hilbert modules and Kasparov modules ⋮ Nonunital spectral triples and metric completeness in unbounded \(KK\)-theory ⋮ The Kasparov product on submersions of open manifolds ⋮ Indefinite Kasparov modules and pseudo-Riemannian manifolds ⋮ Chern numbers, localisation and the bulk-edge correspondence for continuous models of topological phases ⋮ Families of spectral triples and foliations of space(time) ⋮ The KO-valued spectral flow for skew-adjoint Fredholm operators ⋮ The Gromov-Hausdorff propinquity for metric spectral triples ⋮ Sums of regular self-adjoint operators in Hilbert-\(C^{\ast}\)-modules ⋮ Equivariant \(KK\)-theory for non-Hausdorff groupoids ⋮ The two definitions of the index difference ⋮ Riemannian embeddings in codimension one as unbounded \(KK\)-cycles ⋮ Callias-type operators associated to spectral triples ⋮ Homotopy equivalence in unbounded \(KK\)-theory ⋮ Spectral localization for semimetals and Callias operators ⋮ A local global principle for regular operators in Hilbert \(C^*\)-modules ⋮ A Serre-Swan theorem for bundles of bounded geometry ⋮ Riemannian submersions and factorization of Dirac operators ⋮ Factorization of Dirac operators on almost-regular fibrations of \(\mathrm{spin}^c\) manifolds ⋮ On the unbounded picture of \(KK\)-theory ⋮ A \(KK\)-theoretic perspective on deformed Dirac operators ⋮ Locally bounded perturbations and (odd) unbounded $KK$-theory ⋮ Poincaré duality for Cuntz-Pimsner algebras ⋮ The bulk-edge correspondence for the quantum Hall effect in Kasparov theory ⋮ Gauge theory on noncommutative Riemannian principal bundles ⋮ The \(K\)-theoretic bulk-edge correspondence for topological insulators ⋮ Involutive operator algebras ⋮ FACTORISATION OF EQUIVARIANT SPECTRAL TRIPLES IN UNBOUNDED -THEORY ⋮ Lifting spectral triples to noncommutative principal bundles ⋮ The unbounded Kasparov product by a differentiable module ⋮ Immersions and the unbounded Kasparov product: embedding spheres into Euclidean space ⋮ Hecke operators in \(KK\)-theory and the \(K\)-homology of Bianchi groups ⋮ The APS-index and the spectral flow ⋮ Real spectral triples on crossed products
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