New Sasaki–Einstein 5‐manifolds

Abstract

By estimating the δ$\delta$‐invariants of certain log del Pezzo surfaces, we prove that closed simply connected 5‐manifolds 2(S2×S3)#nM2$2(S^2\times S^3)\# nM_2$ allow Sasaki‐Einstein structures, where M2$M_2$ is the closed simply connected 5‐manifold with H2(M2,Z)=double-struckZ/2double-struckZ⊕double-struckZ/2double-struckZ$\mathrm{H}_2(M_2,\mathbb {Z})=\mathbb {Z}/2\mathbb {Z}\oplus \mathbb {Z}/2\mathbb {Z}$, nM2$nM_2$ is the n$n$‐fold connected sum of M2$M_2$, and 2false(S2×S3false)$2(S^2\times S^3)$ is the twofold connected sum of S2×S3$S^2\times S^3$.