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Chern numbers for two families of noncommutative Hopf fibrations

Piotr M. Hajac·Rainer Matthes·Wojciech Szymanski
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Abstract

We consider noncommutative line bundles associated with the Hopf fibrations of SUq(2) over all Podles spheres and with a locally trivial Hopf fibration of S^3_{pq}. These bundles are given as finitely generated projective modules associated via 1-dimensional representations of U(1) with Galois-type extensions encoding the principal fibrations of SUq(2) and S^3_{pq}. We show that the Chern numbers of these modules coincide with the winding numbers of representations defining them.

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Piotr M. Hajac, Rainer Matthes, Wojciech Szymanski. 2003-02-20. Chern numbers for two families of noncommutative Hopf fibrations. https://arxiv.org/abs/math/0302256

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