Differential geometric invariants for time-reversal symmetric Bloch-bundles: The “Real” case

DOI10.1063/1.4948742zbMath1346.57024arXiv1502.01232OpenAlexW1636731964WikidataQ115333181 ScholiaQ115333181MaRDI QIDQ2814227

Kiyonori Gomi, Giuseppe De Nittis

Publication date: 20 June 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.01232

zbMATH Keywords

condensed mattertime reversal symmetrytopological quantum systemsBloch bundlesKR theory

Mathematics Subject Classification ID

Stable classes of vector space bundles in algebraic topology and relations to (K)-theory (55R50) Topological field theories in quantum mechanics (81T45) Applications of global differential geometry to the sciences (53C80) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Topological quantum field theories (aspects of differential topology) (57R56) Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics (82B21) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Topology of vector bundles and fiber bundles (57R22) Equivariant homotopy theory in algebraic topology (55P91) Homotopy and topological questions for infinite-dimensional manifolds (58B05) Homology with local coefficients, equivariant cohomology (55N25)

Related Items

The FKMM-invariant in low dimension, The geometry of (non-abelian) Landau levels, Differential geometric invariants for time-reversal symmetric Bloch bundles. II: The low-dimensional ``quaternionic case, Topological insulators and the Kane–Mele invariant: Obstruction and localization theory, The cohomological nature of the Fu-Kane-Mele invariant, Two-dimensional time-reversal-invariant topological insulators via Fredholm theory, Chiral vector bundles, A non-commutative framework for topological insulators, Differential geometric invariants for time-reversal symmetric Bloch-bundles: The “Real” case, On the K-theoretic classification of dynamically stable systems, Classification of ``quaternionic Bloch-bundles: topological quantum systems of type AII

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