The Cayley transform in complex, real and graded K-theory

Chris Bourne, Johannes Kellendonk, Adam Rennie

Research output: Contribution to journalArticlepeer-review


We use the Cayley transform to provide an explicit isomorphism at the level of cycles from van Daele K-theory to KK-theory for graded C∗-algebras with a real structure. Isomorphisms between KK-theory and complex or real K-theory for ungraded C∗-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 K-theory and topological phases of matter.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2019 Dec 15

ASJC Scopus subject areas

  • General

Fingerprint Dive into the research topics of 'The Cayley transform in complex, real and graded K-theory'. Together they form a unique fingerprint.

Cite this