New Sasaki-Einstein 5-manifolds

Abstract

We prove that closed simply connected $5$-manifolds $2(S^2\times S^3)\#n{M}_2$ allow Sasaki-Einstein structures, where $M_2$ is the closed simply connected $5$-manifold with ${\mathrm{H}}_2(M_2,\mathbb{Z})=\mathbb{Z}/2\mathbb{Z}\oplus \mathbb{Z}/2\mathbb{Z}$, $n{M}_2$ is the $n$-fold connected sum of $M_2$, and $2(S^2\times S^3)$ is the two-fold connected sum of $S^2\times S^3$.

20 pages