Defines analytic index for Clifford anti-linear, skew-adjoint, self-adjoint and odd Fredholm operators on real Hilbert C*-modules and proves a real Robbin-Salamon theorem linking spectral flow to Fredholm index via Van Daele K-theory.
Kubota, Stable homotopy theory of invertible gapped quantum spin systems i: Kitaev’sω-spectrum (2025), arXiv:2503.12618 [math-ph]
5 Pith papers cite this work. Polarity classification is still indexing.
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2026 5representative citing papers
Develops K-theoretic obstruction theory for linearizing QCA representations over arbitrary fields, extracting universal classes and computing homotopy types over point/line/plane in the complex unitary case.
Diabolical textures from spatially embedded Thouless pumps yield distinct gapped states separated by trap-scaling critical points that terminate into unnecessary critical surfaces when the texture varies rapidly, with a classification framework based on Kitaev's Ω spectrum conjecture.
Phase diagrams of trivial phases in class A non-interacting fermions exhibit topological textures from non-trivial state families, computed via higher Berry phases, with diabolical points hosting robust boundary modes.
Homotopy classes of sections of pure-state bundles of the Weyl C*-algebra recover the K-theoretic classification of type-A and AI topological insulators.
citing papers explorer
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Analytic index theory and spectral flow in real Hilbert $C^*$-modules
Defines analytic index for Clifford anti-linear, skew-adjoint, self-adjoint and odd Fredholm operators on real Hilbert C*-modules and proves a real Robbin-Salamon theorem linking spectral flow to Fredholm index via Van Daele K-theory.
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$K$-Theoretic Obstructions to Linearizing QCA Representations
Develops K-theoretic obstruction theory for linearizing QCA representations over arbitrary fields, extracting universal classes and computing homotopy types over point/line/plane in the complex unitary case.
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Topological Phenomena Protected by Diabolical Textures
Diabolical textures from spatially embedded Thouless pumps yield distinct gapped states separated by trap-scaling critical points that terminate into unnecessary critical surfaces when the texture varies rapidly, with a classification framework based on Kitaev's Ω spectrum conjecture.
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Textured phase diagrams of featureless insulators
Phase diagrams of trivial phases in class A non-interacting fermions exhibit topological textures from non-trivial state families, computed via higher Berry phases, with diabolical points hosting robust boundary modes.
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A scheme for topological phases of the Weyl $C^*$-algebra
Homotopy classes of sections of pure-state bundles of the Weyl C*-algebra recover the K-theoretic classification of type-A and AI topological insulators.