The de Rham theorem for the noncommutative complex of Cenkl and Porter.
The Frobenius theorem on -dimensional quantum hyperplane.
The garden of quantum spheres
A list of known quantum spheres of dimension one, two and three is presented.
The Local Index Formula in Noncommutative Geometry.
The scattering problem for a noncommutative nonlinear Schrödinger equation.
Twisted spectral triples and covariant differential calculi
Connes and Moscovici recently studied "twisted" spectral triples (A,H,D) in which the commutators [D,a] are replaced by D∘a - σ(a)∘D, where σ is a second representation of A on H. The aim of this note is to point out that this yields representations of arbitrary covariant differential calculi over Hopf algebras in the sense of Woronowicz. For compact quantum groups, H can be completed to a Hilbert space and the calculus is given by bounded operators. At the end, we discuss an explicit example of...