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Sasaki-Einstein 7-manifolds and Orlik's conjecture
Jaime Cuadros, Joe Lope
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We calculate the homology groups of certain 2-connected 7-manifolds admitting quasi-regular Sasaki-Einstein metrics. These manifolds are links that arise as Thom-Sebastiani sums of chain type singularities and cycle type singularities. Among these links, we found 52 new examples of Sasaki-Einstein rational homology 7-spheres and 124 new examples of Sasaki-Einstein 2-connected 7-manifolds homeomorphic to connected sums of S³ ×S⁴. Furthermore, we found that manifolds of the form k #(S³ ×S⁴) admit Sasaki-Einstein metrics for 22 different values of k. We also describe the diffeomorphism type of certain families of homotopy 9-spheres admitting positive Ricci curvature. These manifolds are branched covers of S¹¹ branched over Sasaki-Einstein rational homology 7-spheres.
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