Classification of tight contact structures on a solid torus

Zhenkun Li; Jessica J. Zhang

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arXiv · 2006.16461

Classification of tight contact structures on a solid torus

Zhenkun Li·Jessica J. Zhang

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Abstract

It is a basic question in contact geometry to classify all non-isotopic tight contact structures on a given 3-manifold. If the manifold has a boundary, we need also specify the dividing set on the boundary. In this paper, we answer the classification question completely for the case of a solid torus by writing down a closed formula for the number of non-isotopic tight contact structures with any given dividing set on the boundary of the solid torus. Previously, only a few special cases were known due to work by Honda.

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Zhenkun Li, Jessica J. Zhang. 2020-06-30. Classification of tight contact structures on a solid torus. https://arxiv.org/abs/2006.16461

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