Classification of tight contact structures on a solid torus

Zhenkun Li, Jessica Zhang

Published 2020-06-30Version 1

It is a basic question in contact geometry to classify all nonisotopic tight contact structures on a given 3-manifold. If the manifold has a boundary, then 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 nonisotopic tight contact structures for any possible dividing set on the boundary of the solid torus. Previously only some special cases were known due to work of Honda in 2000 and Honda, Kazez, and Mati\'c in 2002.