Trieste, August 26-28 2014

K-homology and graph algebras

Gysin Sequences and Pimsner Algebras

Starting from a C*-correspondence E over a C*-algebra A, we construct the corresponding Pimsner algebra, that we understand as the total space algebra of a principal circle bundle over A. A natural six term exact sequence relates the KK-theories of the Pimsner Algebra with those of A. This exact sequence is an analogue of the Gysin Sequence for circle bundles. Interesting examples come from line bundles over a quantum weighted projective line (with arbitrary weights).