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A proof of Bott periodicity via Quot schemes and bulk-edge correspondence (2403.00342v1)
Published 1 Mar 2024 in math.KT, math-ph, math.AT, and math.MP
Abstract: In this paper, we give alternative proofs of Bott periodicity of $ K $-theory and the bulk-edge correspondence of integer quantum Hall effect. Regarding Bott periodicity, we connect its proof with configuration spaces and use Quot schemes in algebraic geometry in our proof. Regarding the bulk-edge correspondence, we formulate edge indices based on the consideration of Graf--Porta and give a more elementary and self-contained proof.
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