  It is shown that the isospectral bi-equivariant spectral triple on quantum
SU(2) and the isospectral equivariant spectral triples on the Podles spheres
are related by restriction. In this approach, the equatorial Podles sphere is
distinguished because only in this case the restricted spectral triple admits
an equivariant grading operator together with a real structure (up to
infinitesimals of arbitrary high order). The real structure is expressed by the
Tomita operator on quantum SU(2) and it is shown that the failure of the real
structure to satisfy the commutant property is related to the failure of the
universal R-matrix operator to be unitary.
