Many noncommutative spaces are constructed by considering a deformation of a (commutative) manifold. It turns out that many properties of these noncommutative spaces resemble closely that of their commutative counterparts: spectral properties, spin structures and their K-theory. Somewhat suprisingly given the these facts, the fine structure of principal circle bundles and their associated line bundles of a noncommutative space can be very different from that of its undeformed counterpart.

 

In this talk we will discuss some examples of this phenomenon, namely quantum lens spaces and theta-deformed spheres, and show some applications of these ``exotic'' bundles.

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