Sasaki–Einstein 7-manifolds and Orlik’s conjecture
Jaime Cuadros Valle,
Joe Lope Vicente
Abstract:We study the homology groups of certain 2-connected 7-manifolds admitting quasiregular Sasaki-Einstein metrics, among them, we found 52 new examples of Sasaki-Einstein rational homology 7-spheres, extending the list given by Boyer, Galicki and Nakamaye in [6]. As a consequence, we exhibit new families of positive Sasakian homotopy 9-spheres given as cyclic branched covers, determine their diffeomorphism types and find out which elements do not admit extremal Sasaki metrics. We also improve previous results giv… Show more
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