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Quantum Bundle Description of Quantum Projective Spaces, Comm. Math. Phys., 316, 345–373, (2012)
Quantum projective N-space, endowed with the Heckenberger-Kolb first-order differential calculus, is presented as the base of a quantum principal bundle. This allows for the construction of connection form which generalises the well known q-monopole connection on the standard Podles sphere.
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Noncommutative Complex Structures on Quantum Homogeneous Spaces, (to appear in J. Geom. Phys.)
A new framework for doing noncommutative complex geometry on quantum homogeneous spaces is introduced. The motivating example is quantum projective N-space, endowed with the Heckenberger-Kolb first-order differential calculus.
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The Noncommutative Kähler Geometry of the Standard Podles Sphere, arXiv:1401.1459
For the standard Podles sphere, endowed with its standard differential calculus, there are presented direct q-generalisations of Hodge decomposition, Lefschetz decomposition, the Kähler identities, and the refinement of de Rham cohomology by Dolbeault cohomology.