Anti-selfdual Connections on the Quantum Projective Plane: Monopoles

Details Anti-selfdual Connections on the Quantum Projective Plane: Monopoles Anti-selfdual Connections on the Quantum Projective Plane: Monopoles

2009-03-20

arxiv.org/abs/0903.3551v2

Commun. Math. Phys. 297 (2010) 841-893

Mathematics

Quantum Algebra

dcpic, pdflatex. v2: 51 pages. Added a Section of Concluding remarks, an Appendix on representations of the coordinate algebra

Scientific paper

10.1007/s00220-010-1057-0

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.

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