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