Abstract
We present several results on the geometry of the quantum projective plane. 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 ‘classical’ characteristic classes (via Fredholm modules); complete diagonalization of gauged Laplacians on these line bundles; ‘quantum’ characteristic classes via equivariant K-theory and q-indices.
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Communicated by A. Connes
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D’Andrea, F., Landi, G. Anti-Selfdual Connections on the Quantum Projective Plane: Monopoles. Commun. Math. Phys. 297, 841–893 (2010). https://doi.org/10.1007/s00220-010-1057-0
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DOI: https://doi.org/10.1007/s00220-010-1057-0