Sasakian-Einstein Structures on 9#(S^2\times S^3)
Abstract
We show that \scriptstyle{#9(S^2\times S^3)} admits an 8-dimensional complex family of inequivalent non-regular Sasakian-Einstein structures. These are the first known Einstein metrics on this 5-manifold. In particular, the bound \scriptstyle{b_2(M)\leq8} which holds for any regular Sasakian-Einstein \scriptstyle{M} does not apply to the non-regular case. We also discuss the failure of the Hitchin-Thorpe inequality in the case of 4-orbifolds and describe the orbifold version.