English

Bott periodicity and almost commuting matrices

K-Theory and Homology 2019-01-15 v1 Operator Algebras

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.

Keywords

Cite

@article{arxiv.1901.03774,
  title  = {Bott periodicity and almost commuting matrices},
  author = {Rufus Willett},
  journal= {arXiv preprint arXiv:1901.03774},
  year   = {2019}
}

Comments

15 pages

R2 v1 2026-06-23T07:09:32.609Z