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arXiv · 1304.3662

Orderable Contact Structures on Liouville-fillable Contact Manifolds

Peter Weigel
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Abstract

We study the existence of positive loops of contactomorphisms on a Liouville-fillable contact manifold $(Σ,ξ=\ker(α))$. Previous results show that a large class of Liouville-fillable contact manifolds admit contractible positive loops. In contrast, we show that for any Liouville-fillable $(Σ,α)$ with $\dim(Σ) \geq 7$, there exists a Liouville-fillable contact structure $ξ'$ on $Σ$ which admits no positive loop at all. Further, $ξ'$ can be chosen to agree with $ξ$ on the complement of a Darboux ball.

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Peter Weigel. 2013-04-12. Orderable Contact Structures on Liouville-fillable Contact Manifolds. https://arxiv.org/abs/1304.3662

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