Graded $K$-theory and $K$-homology of relative Cuntz-Pimsner algebras and graph $C^{\ast }$-algebras

Abstract

We establish exact sequences in $KK$-theory for graded relative Cuntz-Pimsner algebras associated to nondegenerate $C^{\ast }$-correspondences. We use this to calculate the graded $K$-theory and $K$-homology of relative Cuntz-Krieger algebras of directed graphs for gradings induced by $\{0,1\}$-valued labellings of their edge sets.

24 pages

References in corpus (3)

• Adding tails to C*-correspondences
• Fredholm modules over graph C*-algebras
• Honours thesis: Exact sequences in graded $KK$-theory for Cuntz-Pimsner algebras