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We study the geometry and topology of two infinite families Y^{p,k} ofSasaki-Einstein seven-manifolds, that are expected to be AdS_4/CFT_3 dual tofamilies of N=2 superconformal field theories in three dimensions. Thesemanifolds, labelled by two positive integers p and k, are Lens space bundlesS^3/Z_p over CP^2 and CP^1 x CP^1, respectively. The corresponding Calabi-Yaucones are toric. We present their toric diagrams and gauged linear sigma modelcharges in terms of p and k, and find that the Y^{p,k} manifolds interpolatebetween certain orbifolds of the homogeneous spaces S^7, M^{3,2} and Q^{1,1,1}.

Notes on toric Sasaki-Einstein seven-manifolds and AdS_4/CFT_3