We construct spectral triples on all Podleś quantum spheres S2qt. These noncommutative geometries are equivariant for a left action of q(su(2)) and are regular, even and of metric dimension 2. They are all isospectral to the undeformed round geometry of the sphere S2. There is also an equivariant real structure for which both the commutant property and the first order condition for the Dirac operators are valid up to infinitesimals of arbitrary order.
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Giovanni Landi, Elmar Wagner, Ludwik Dąbrowski, Francesco D'Andrea, Dirac operators on all Podleś quantum spheres. J. Noncommut. Geom. 1 (2007), no. 2, pp. 213–239DOI 10.4171/JNCG/5