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arXiv · 1901.03774

Bott periodicity and almost commuting matrices

Rufus Willett
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Abstract

We give a proof of the Bott periodicity theorem for topological K-theory of C*-algebras based on Loring's treatment of Voiculescu's almost commuting matrices and Atiyah's rotation trick. We also explain how this relates to the Dirac operator on the circle; this uses Yu's localization algebra and an associated explicit formula for the pairing between the first K-homology and first K-theory groups of a (separable) C*-algebra.

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Rufus Willett. 2019-01-12. Bott periodicity and almost commuting matrices. https://arxiv.org/abs/1901.03774

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