---
abstract: |
    We generalize to quantum weighted projective spaces in any dimension previous results of us on K-theory and K-homology of quantum projective spaces ‘tout court’. For a class of such spaces, we explicitly construct families of Fredholm modules, both bounded and unbounded (that is spectral triples), and prove that they are linearly independent in the K-homology of the corresponding $C^*$-algebra. We also show that the quantum weighted projective spaces are base spaces of quantum principal circle bundles whose total spaces are quantum lens spaces. We construct finitely generated projective modules associated with the principal bundles and pair them with the Fredholm modules, thus proving their non-triviality.

    *Dedicated to Marc Rieffel on the occasion of his 75th birthday*
address:
- 'Dipartimento di Matematica e Applicazioni, Università di Napoli “Federico II” and I.N.F.N. Sezione di Napoli, Complesso MSA, Via Cintia, 80126 Napoli, Italy'
- 'Matematica, Università di Trieste, Via A. Valerio 12/1, I-34127 Trieste, Italy and I.N.F.N. Sezione di Trieste, Trieste, Italy.'
author:
- 'Francesco D’Andrea and Giovanni Landi'
title: Quantum weighted projective and lens spaces
---

Introduction {#se:intro}
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This paper deals with the geometry of quantum *weighted* projective spaces. For any weight vector ${\underline}{\ell}=(\ell_0,\ldots,\ell_n)$, the quantum weighted projective 