Sasaki-Einstein 7-Manifolds, Orlik Polynomials and Homology

2016/07/30 by Gomez, Ralph R.
#Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1608.00564

Abstract

Let L_f be a link of an isolated hypersurface singularity defined by a weighted homogenous polynomial f. In this article, we give ten examples of 2-connected seven dimensional Sasaki-Einstein manifolds L_f for which H₃(L_f, ℤ) is completely determined. Using the Boyer-Galicki construction of links L_f over particular Kähler-Einstein orbifolds, we apply a valid case of Orlik's conjecture to the links L_f so that one is able to explicitly determine H₃(L_f,ℤ). We give ten such new examples, all of which have the third Betti number satisfy 10≤ b₃(L_f)≤ 20.

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