Anti-selfdual Connections on the Quantum Projective Plane: Monopoles

Abstract

We present several results on the geometry of the quantum projective plane CP2q. They include: explicit generators for the K-theory and the K-homology; a real calculus with a Hodge star operator; anti-selfdual connections on line bundles with explicit computation of the corresponding 'monopoles' and 'instanton' charges; complete diagonalization of gauged Laplacians on these line bundles; quantum invariants via equivariant K-theory and q-indices.

dcpic, pdflatex. v2: 51 pages. Added a Section of Concluding remarks, an Appendix on representations of the coordinate algebra of the quantum projective plane and three additional references. Several minor changes throughout the paper including changes in terminology. To appear in CMP.

References in corpus (6)

• Dirac Operators on Quantum Projective Spaces
• The Noncommutative Geometry of the Quantum Projective Plane
• Gauged Laplacians on quantum Hopf bundles
• Bounded and unbounded Fredholm modules for quantum projective spaces
• The Isospectral Dirac Operator on the 4-dimensional Orthogonal Quantum Sphere
• On the noncommutative spin geometry of the standard Podles sphere and index computations

Cited by in corpus (13)

• Dirac Operators on Quantum Projective Spaces
• Noncommutative complex geometry of the quantum projective space
• The homogeneous coordinate ring of the quantum projective plane
• Quantum Bundle Description of the Quantum Projective Spaces
• Calculi, Hodge operators and Laplacians on a quantum Hopf fibration
• Positive Line Bundles Over the Irreducible Quantum Flag Manifolds
• Anti-selfdual Connections On The Quantum Projective Plane: Instantons
• Differential and Twistor Geometry of the Quantum Hopf Fibration
• Warped Products and Yang-Mills equations on non commutative spaces
• The Quantum Flag Manifold $\mathbf{S}{\mathbf{U}}_{\mathbf{q}}(3)/{\mathbb{T}}^2$ as an Example of a Noncommutative Sphere Bundle
• Geometry of the quantum projective plane
• Differential and holomorphic differential operators on noncommutative algebras
• Twisted sigma-model solitons on the quantum projective line