Quantum weighted projective and lens spaces

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.

30 pages, no figures. Section on spectral triples expanded with some new results

References in corpus (3)

• Pimsner algebras and Gysin sequences from principal circle actions
• The Noncommutative Geometry of the Quantum Projective Plane
• The Gysin Sequence for Quantum Lens Spaces

Cited by in corpus (9)

• The geometry of quantum lens spaces: real spectral triples and bundle structure
• Notes on quantum weighted projective spaces and multidimensional teardrops
• Pimsner algebras and circle bundles
• Differential Calculi on Quantum Principal Bundles over Projective Bases
• Topics in Noncommutative Geometry
• Quantum spheres as graph C*-algebras: a review
• Veronese and Segre morphisms between non-commutative projective spaces
• On The Classification of Quantum Lens Spaces of Dimension at most 7
• Gysin exact sequences for quantum weighted lens spaces