Gysin exact sequences for quantum weighted lens spaces

TL;DR

This paper develops a noncommutative Gysin sequence for quantum weighted lens spaces, enabling the computation of their K-theory and K-homology groups using a Cuntz-Pimsner model.

Contribution

It introduces a noncommutative Gysin exact sequence for quantum weighted lens spaces and applies it to compute their K-theory and K-homology groups.

Findings

Computed K-theory groups of quantum weighted lens spaces

Extended previous results on quantum lens spaces

Established a noncommutative Gysin sequence framework

Abstract

We describe quantum weighted lens spaces as total spaces of quantum principal circle bundles, using a Cuntz-Pimsner model. The corresponding Pimsner exact sequence is interpreted as a noncommutative analogue of the Gysin exact sequence. We use the sequence to compute the K-theory and K-homology groups of quantum weighted lens spaces, extending previous results and computations due to the author and collaborators.