English

Formality of 7-dimensional 3-Sasakian manifolds

Differential Geometry 2015-12-01 v1

Abstract

We prove that any simply connected compact 3-Sasakian manifold, of dimension seven, is formal if and only if its second Betti number is b2<2b_2<2. In the opposite, we show an example of a 7-dimensional Sasaki-Einstein manifold, with second Betti number b22b_2\geq 2, which is formal. Therefore, such an example does not admit any 3-Sasakian structure. Examples of 7-dimensional simply connected compact formal Sasakian manifolds, with b22b_2\geq 2, are also given.

Keywords

Cite

@article{arxiv.1511.08930,
  title  = {Formality of 7-dimensional 3-Sasakian manifolds},
  author = {Marisa Fernández and Stefan Ivanov and Vicente Muñoz},
  journal= {arXiv preprint arXiv:1511.08930},
  year   = {2015}
}

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10 pages