Geometry of the quantum projective plane

TL;DR

This paper explores the geometric structure of the quantum projective plane, focusing on differential calculus, Dirac operators, anti-self-dual connections, and characteristic classes in a quantum setting.

Contribution

It introduces a differential calculus and Dirac operator on the quantum projective plane, advancing the understanding of its geometric and topological properties.

Findings

Construction of a differential calculus on the quantum projective plane

Development of a Dirac operator with a spin^c-structure

Analysis of anti-self-dual connections and spectrum of Laplacians

Abstract

We review some of the geometry of the quantum projective plane with emphasis on the construction of a differential calculus and of the Dirac operator (of a spin^c-structure). We also report on anti-self-dual connections on line bundles, the spectrum of associated (gauged) Laplacian operators, and on classical and quantum characteristic classes.