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 in K-theory. We use the sequence to compute the
K-theory 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.
