Topological Band Theory for High-Dimensional Parameter Spaces

arXiv:2609.35977 · cond-mat.mes-hall, hep-th, math-ph, math.AG, math.MP, quant-ph · Submitted 2026-09-28 · Read on arXiv

cond-mat.mes-hall, hep-th, math-ph, math.AG, math.MP, quant-ph

Submitted: 2026-09-28

Updated: 2026-09-28

Comments: 24 pages, 4 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Quantization — 12× in this paper · explained in 12 episodes
• Generalization — 9× in this paper · explained in 13 episodes
• Berry Curvature — 8× in this paper · explained in 3 episodes
• Holonomy — 6× in this paper · explained in 2 episodes
• Chern Number — 4× in this paper · explained in 4 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Accuracy — 1× in this paper · explained in 1 episode
• Degeneracy — 1× in this paper · explained in 3 episodes
• Topological Order — 1× in this paper · explained in 2 episodes

Sources

• On the hyperbolic Bloch transform
• Beyond $K$-Theory: Geometry and Holomorphy in Hyperbolic Band Theory
• 6D Fractional Quantum Hall Effect
• A Four Dimensional Generalization of the Quantum Hall Effect
• Quantum Hall Effect in Higher Dimensions
• ADHM and the 4d Quantum Hall Effect
• Lectures on the Quantum Hall Effect
• Topological linear response of hyperbolic Chern insulators

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