Some examples of toric Sasaki-Einstein manifolds

Craig van Coevering

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Some examples of toric Sasaki-Einstein manifolds

Craig van Coevering

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Abstract

A series of examples of toric Sasaki-Einstein 5-manifolds is constructed. These are submanifolds of toric 3-Sasaki 7-manifolds and such a Sasaki-Einstein 5-manifold corresponds uniquely to a toric 3-Sasaki 7-manifold. This produces examples of quasi-regular Sasaki-Einstein structures on every #k(S^2 xS^3), for k odd. Toric geometry is used to construct examples of positive Ricci curvature toric Sasaki structures on non-spin 5-manifolds. Then the join construction is used to construct infinitely many quasi-regular toric Sasaki-Einstein manifolds with arbitrarily high second Betti number in every odd dimesion >3.

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Craig van Coevering. 2007-03-16. Some examples of toric Sasaki-Einstein manifolds. https://arxiv.org/abs/math/0703501

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