We give new examples of noncommutative manifolds that are less standard than the NC-torus or Moyal deformations of R. They arise naturally from basic considerations of noncommutative differential… (More)

We construct spectral triples on all Podleś quantum spheres S qt. These noncommutative geometries are equivariant for a left action of Uq(su(2)) and are regular, even and of metric dimension 2. They… (More)

We construct noncommutative principal fibrations S7 θ → S4 θ which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated… (More)

We construct a quantum version of the SU(2) Hopf bundle S7 → S4. The quantum sphere S7 q arises from the symplectic group Spq(2) and a quantum 4sphere S4 q is obtained via a suitable self-adjoint… (More)

We construct an approximation to field theories on the noncommutative torus based on soliton projections and partial isometries which together form a matrix algebra of functions on the sum of two… (More)

We present an approximation to topological spaces by noncommutative lattices. This approximation has a deep physical flavour based on the impossibility to fully localize particles in any position… (More)

We construct a new gauge theory on a pair of d-dimensional noncommutative tori. The latter comes from an intimate relationship between the noncommutative geometry associated with a lattice vertex… (More)

The eigenvalues of the Dirac operator on a curved spacetime are diffeomorphism-invariant functions of the geometry. They form an infinite set of “observables” for general relativity. Recent work of… (More)

In the spirit of noncommutative geometry we construct all inequivalent vector bundles over the (2, 2)-dimensional supersphere S2,2 by means of global projectors p via equivariant maps. Each projector… (More)