# Pimsner algebras and Gysin sequences from principal circle actions

### Francesca Arici

Radboud University Nijmegen, Netherlands### Jens Kaad

Radboud University Nijmegen, Netherlands### Giovanni Landi

Università di Trieste, Italy

## Abstract

A self Morita equivalence over an algebra $B$, given by a $B$-bimodule $E$, is thought of as a line bundle over $B$. The corresponding Pimsner algebra $\mathcal O_E$ is then the total space algebra of a noncommutative principal circle bundle over $B$. A natural Gysin-like sequence relates the $KK$-theories of $\mathcal O_E$ and of $B$. Interesting examples come from $\mathcal O_E$ a quantum lens space over $B$ a quantum weighted projective line (with arbitrary weights). The $KK$-theory of these spaces is explicitly computed and natural generators are exhibited.

## Cite this article

Francesca Arici, Jens Kaad, Giovanni Landi, Pimsner algebras and Gysin sequences from principal circle actions. J. Noncommut. Geom. 10 (2016), no. 1, pp. 29–64

DOI 10.4171/JNCG/228