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

Chris Bourne, Johannes Kellendonk, Adam Rennie

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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
Article number2050074
JournalInternational Journal of Mathematics
Issue number9
Publication statusPublished - 2020 Aug 1


  • K -theory
  • operator algebras
  • topological phases

ASJC Scopus subject areas

  • Mathematics(all)


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