A proof of Bott periodicity via Quot schemes and bulk-edge correspondence

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.