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In this overview, we study how to reduce the index pairing for a fibre-product C*-algebra to the index pairing for the C*-algebra over which the fibre product is taken. As an example we analyze the case of suspensions and apply it to noncommutative instanton bundles of arbitrary charges over the suspension of quantum deformations of the 3-sphere., Comment: 18 pages, to appear in Banach Centre Publications. New title, one more author, totally rewritten with new material added

We describe a locally trivial quantum principal U(1)-bundle over the quantum space S^2_{pq} which is a noncommutative analogue of the usual Hopf bundle. We also provide results concerning the structure of its total space algebra (irreducible *-representations and topological K-groups) and its Galois aspects (Galois property, existence of a strong connection, non-cleftness)., Comment: 5 pages, Latex2e

We consider two Z/2Z-actions on the Podles generic quantum spheres. They yield, as noncommutative quotient spaces, the Klimek-Lesniewski q-disc and the quantum real projective space, respectively. The C*-algebras of all these quantum spaces are described as graph C*-algebras. The K-groups of the thus presented C*-algebras are then easily determined from the general theory of graph C*-algebras. For the quantum real projective space, we also recall the classification of the classes of irreducible *-representations of its algebra and give a linear basis for this algebra., Comment: 8 pages, latex2e

Following ideas of Connes and Moscovici, we describe two spectral triples related to the Kronecker foliation, whose generalized Dirac operators are related to first and second order signature operators. We also consider the corresponding differential calculi $\Omega_D$, which are drastically different in the two cases. As a side-remark, we give a description of a known calculus on the two-dimensional noncommutative torus in terms of generators and relations., Comment: 27 pages

The irreducible *-representations of the polynomial algebra O(S^3_{pq}) of the quantum 3-sphere introduced by Calow and Matthes are classified. The K-groups of its universal C*-algebra are shown to coincide with their classical counterparts. The U(1)-action on O(S^3_{pq}) corresponding for p=1=q to the classical Hopf fibration is proven to be Galois (free). The thus obtained locally trivial Hopf-Galois extension is shown to be relatively projective (admitting a strong connection) and non-cleft. The latter is proven by determining an appropriate Chern-Connes pairing., Comment: latex 2e, 23 pages in A4

Extending work of Budzynski and Kondracki, we investigate coverings and gluings of algebras and differential algebras. We describe in detail the gluing of two quantum discs along their classical subspace, giving a C*-algebra isomorphic to a certain Podles sphere, as well as the gluing of U_{\sqrt{q}}(sl_2)-covariant differential calculi on the discs., Comment: latex2e, 27 pages

The paper covers known facts about the Dixmier trace (with some generalities about traces), the Wodzicki residue, and Connes' trace theorem, including two variants of proof of the latter. Action formulas are treated very sketchy, because they were considered in other lectures of the workshop., Comment: Latex2e, 32 pages, expanded version of a lecture at the workshop "The Standard Model of Elementary Particle Physics from a Mathematical-Geometrical Viewpoint", Hesselberg, March 1999, http://www.uni-leipzig.de/~ntz/abs/abs1299.htm, revised version

We construct a quantum frame bundle of the quantum plane $C^2_p$ by requiring that a $GL_{q,p}(2)$-covariant differential calculus on $C^2_p$ be isomorphic as a bimodule to the space of sections of the associated quantum cotangent bundle. We also construct the section space of the associated quantum tangent bundle, and show that it is naturally dual to the differential calculus., Comment: 8 pages, latex

The effect of 3-G conditions on the bone-to-ligament junctions of the knee is studied in rats. Results following chronic 3-G centrifugation of rats show that their bone-to-ligament junctions exhibited a force-sustaining capacity (F) which was 95 + or - 12% of the value for the control group. However, F was actually 29 + or - 5% greater for centrifuged rats than for control rats of comparable size, as the experimental animals grew to smaller body mass. It is concluded that gravity determines part of the magnitude of F, and therefore this value will probably be weaker after development in a weightless environment.