Chern numbers for two families of noncommutative Hopf fibrations. (English. Abridged French version) Zbl 1029.46112
Summary: We consider noncommutative line bundles associated with the Hopf fibrations of \(\text{SU}_q(2)\) over all Podleś spheres and with a locally trivial Hopf fibration of \(\text{S}^3_{pq}\). These bundles are given as finitely generated projective modules associated via 1-dimensional representations of \(\text{U}(1)\) with Galois-type extensions encoding the principal fibrations of \(\text{SU}_q(2)\) and \(\text{S}^3_{pq}\). We show that the Chern numbers of these modules coincide with the winding numbers of representations defining them.
MSC:
| 46L85 | Noncommutative topology |
| 58B34 | Noncommutative geometry (à la Connes) |
| 16W30 | Hopf algebras (associative rings and algebras) (MSC2000) |
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