In this article, we give ten examples of 2-connected seven dimensional Sasaki-Einstein manifolds for which the third homology group is completely determined. Using the Boyer-Galicki construction of links over particular Kähler-Einstein orbifolds, we apply a valid case of Orlik’s conjecture to the links so that one is able to explicitly determine the entire third integral homology group. We give ten such new examples, all of which have the third Betti number satisfy 10 ≤ b₃ (Lf) ≤ 20 .
Sasaki-Einstein, Kähler 2, orbifolds, links
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Ralph R. Gomez.
"Sasaki-Einstein 7-Manifolds, Orlik Polynomials And Homology".