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arXiv · 1207.2046

Contact Structures on G_2-Manifolds and Spin 7-Manifolds

M. Firat Arikan·Hyunjoo Cho·Sema Salur
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Abstract

We show that there exist infinitely many pairwise distinct non-closed G_2-manifolds (some of which have holonomy full G_2) such that they admit co-oriented contact structures and have co-oriented contact submanifolds which are also associative. Along the way, we prove that there exists a tubular neighborhood N of every orientable three-submanifold Y of an orientable seven-manifold with spin structure such that for every co-oriented contact structure on Y, N admits a co-oriented contact structure such that Y is a contact submanifold of N. Moreover, we construct infinitely many pairwise distinct non-closed seven-manifolds with spin structures which admit co-oriented contact structures and retract onto co-oriented contact submanifolds of co-dimension four.

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M. Firat Arikan, Hyunjoo Cho, Sema Salur. 2012-07-09. Contact Structures on G_2-Manifolds and Spin 7-Manifolds. https://arxiv.org/abs/1207.2046

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