Notes on twisted equivariant K-theory for C*-algebras

DOI10.1142/S0129167X16500580zbMath1347.19001arXiv1511.05312MaRDI QIDQ5739777

Yosuke Kubota

Publication date: 20 July 2016

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.05312

zbMATH Keywords

groupoids\(KK\)-theorytwisted \(K\)-theorytopological insulators

Mathematics Subject Classification ID

Noncommutative geometry in quantum theory (81R60) Kasparov theory ((KK)-theory) (19K35) Equivariant (K)-theory (19L47) Twisted (K)-theory; differential (K)-theory (19L50)

Related Items (13)

The index theorem of lattice Wilson-Dirac operators via higher index theory ⋮ Locally equivalent quasifree states and index theory ⋮ Index theory and topological phases of aperiodic lattices ⋮ Crystallographic T-duality ⋮ Bulk-edge correspondence and the cobordism invariance of the index ⋮ The Cayley transform in complex, real and graded K-theory ⋮ Crystallographic bulk-edge correspondence: glide reflections and twisted mod 2 indices ⋮ Controlled topological phases and bulk-edge correspondence ⋮ Classification of topological invariants related to corner states ⋮ Twisted crystallographic T-duality via the Baum–Connes isomorphism ⋮ Twists on the torus equivariant under the 2-dimensional crystallographic point groups ⋮ The \(K\)-theoretic bulk-edge correspondence for topological insulators ⋮ The bulk–dislocation correspondence for weak topological insulators on screw–dislocated lattices

Cites Work

• Controlled topological phases and bulk-edge correspondence
• A groupoid approach to C*-algebras
• The Novikov conjecture for hyperbolic foliations
• On graded \(K\)-theory, elliptic operators and the functional calculus
• On the \(C^*\)-algebraic approach to topological phases for insulators
• Graded Brauer groups and K-theory with local coefficients
• A non-commutative framework for topological insulators
• Twists over étale groupoids and twisted vector bundles
• Twisted K-theory of differentiable stacks
• Loop groups and twisted K -theory I
• Periodic table for topological insulators and superconductors
• Morphismes $K$-orientés d'espaces de feuilles et fonctorialité en théorie de Kasparov (d'après une conjecture d'A. Connes)
• Operator 𝐾-theory for groups which act properly and isometrically on Hilbert space
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