Sasaki-Einstein 5-manifolds associated to toric 3-Sasaki manifolds
Differential Geometry
2012-08-09 v3
Abstract
We give a correspondence between toric 3-Sasaki 7-manifolds S and certain toric Sasaki-Einstein 5-manifolds M. These 5-manifolds are all diffeomorphic to k#(S^2\times S^3), where k=2b_2(S)+1, and are given by a pencil of Sasaki embeddings of M in S and are given concretely by the zero set of a component of the 3-Sasaki moment map. It follows that there are infinitely many examples of these toric Sasaki-Einstein manifolds M for each odd b_2(M)>1. As an application of the proof of the above, we prove that the local deformation space of ASD structures on a compact toric ASD Einstein orbifold is given by Joyce ansatz conformal metrics.
Keywords
Cite
@article{arxiv.math/0607721,
title = {Sasaki-Einstein 5-manifolds associated to toric 3-Sasaki manifolds},
author = {Craig van Coevering},
journal= {arXiv preprint arXiv:math/0607721},
year = {2012}
}
Comments
final corrections made