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