Chern numbers for two families of noncommutative Hopf fibrations

Hajac, Piotr M.; Matthes, Rainer; Szymanski, Wojciech

Chern numbers for two families of noncommutative Hopf fibrations

Authors

Hajac, Piotr M.

Matthes, Rainer

Szymanski, Wojciech

Description

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.
6 pages