Nontrivial Holomorphic Structures on the Quantum Sphere

The area of Noncommutative Geometry is quite new, and even newer is the concept of a complex structure in Noncommutative Geometry. In previous literature, various complex structures have been defined within the noncommutative framework, with various results found, including the Quantum Sphere. However, all previous investigations into the structure of the Quantum Sphere have always found its algebraic and analytic properties to be not too dissimilar from the classical Riemann Sphere. Here, we demonstrate that in regard to holomorphic structures that can be defined on the space, the Quantum Sphere is indeed very different from the Riemann Sphere.

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