Geometry of the quantum projective plane

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.

v2: one very minor change. 18 pages, amsart, dcpic. Based on invited talks at the Satellite Conference to the 5th European Congress of Mathematics: "Noncommutative structures in Mathematics and Physics", Royal Flemish Academy, Brussels (Belgium), 22-26 July 2008. Published in the Proceedings

References in corpus (3)

• On the spectral characterization of manifolds
• Anti-selfdual Connections on the Quantum Projective Plane: Monopoles
• The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere

Cited by in corpus (1)

• Anti-selfdual Connections On The Quantum Projective Plane: Instantons