English

Classification of tight contact structures on a solid torus

Geometric Topology 2020-07-24 v3

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.

Keywords

Cite

@article{arxiv.2006.16461,
  title  = {Classification of tight contact structures on a solid torus},
  author = {Zhenkun Li and Jessica J. Zhang},
  journal= {arXiv preprint arXiv:2006.16461},
  year   = {2020}
}

Comments

19 pages, 11 figures; fixed an error in previous versions

R2 v1 2026-06-23T16:43:14.401Z