The Cayley transform in complex, real and graded $K$-theory
K-Theory and Homology
2020-06-09 v2 Mathematical Physics
math.MP
Operator Algebras
Abstract
We use the Cayley transform to provide an explicit isomorphism at the level of cycles from van Daele -theory to -theory for graded -algebras with a real structure. Isomorphisms between -theory and complex or real -theory for ungraded -algebras are a special case of this map. In all cases our map is compatible with the computational techniques required in physical and geometrical applications, in particular index pairings and Kasparov products. We provide applications to real -theory and topological phases of matter.
Cite
@article{arxiv.1912.07158,
title = {The Cayley transform in complex, real and graded $K$-theory},
author = {Chris Bourne and Johannes Kellendonk and Adam Rennie},
journal= {arXiv preprint arXiv:1912.07158},
year = {2020}
}
Comments
v2: 43 pages, minor revisions. To appear in Internat. J. Math