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.

__About the speaker:__

Giovanni Landi is a professor of mathematical physics at Universita di Trieste.

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