We study a three-dimensional differential calculus on the standard Podles
quantum two-sphere S^2_q, coming from the Woronowicz 4D+ differential calculus
on the quantum group SU_q(2). We use a frame bundle approach to give an
explicit description of the space of forms on S^2_q and its associated spin
geometry in terms of a natural spectral triple over S^2_q. We equip this
spectral triple with a real structure for which the commutant property and the
first order condition are satisfied up to infinitesimals of arbitrary order.Comment: v2: 25 pages; minor change
