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arXiv · 2208.10666

Sasaki-Einstein 7-manifolds and Orlik's conjecture

Jaime Cuadros·Joe Lope
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Abstract

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 $S^{3} \times S^{4}.$ Furthermore, we found that manifolds of the form $k \#\left(S^{3} \times S^{4}\right)$ 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 $S^{11}$ branched over Sasaki-Einstein rational homology 7-spheres.

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Jaime Cuadros, Joe Lope. 2022-08-23. Sasaki-Einstein 7-manifolds and Orlik's conjecture. https://doi.org/10.1007/s10455-023-09930-z

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