# The Gysin sequence for quantum lens spaces

### Francesca Arici

Radboud University Nijmegen, Netherlands### Simon Brain

Radboud Universiteit Nijmegen, Netherlands### Giovanni Landi

Università di Trieste, Italy

## 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.

## Cite this article

Francesca Arici, Simon Brain, Giovanni Landi, The Gysin sequence for quantum lens spaces. J. Noncommut. Geom. 9 (2015), no. 4, pp. 1077–1111

DOI 10.4171/JNCG/216