Classification of tight contact structures on a solid torus
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2020
- DOI:
- 10.48550/arXiv.2006.16461
- arXiv:
- arXiv:2006.16461
- Bibcode:
- 2020arXiv200616461L
- Keywords:
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- Mathematics - Geometric Topology;
- 57K33 (Primary) 57M50 (Secondary)
- E-Print:
- 19 pages, 11 figures