The $KK$-theory of quantum lens spaces

Giovanni Landi  (Universita di Trieste)

8:30 am to 9:20 am, June 2nd, 2015   Science Building A510

Abstract:

We define quantum lens spaces as 'direct sums of line bundles' and exhibit them as 'total spaces' of certain principal bundles over quantum projective spaces. For each of these quantum lens spaces we construct an analogue of the classical Gysin sequence. We use the sequence to compute the $K$-theory and the $K$-homology of the quantum lens spaces, in particular to give explicit geometric representatives of their $K$-theory classes. These representatives are interpreted as 'line bundles' over quantum lens spaces and generically define 'torsion classes'. We work out explicit examples of these classes.