Classification of Tight Contact Structures on a Solid Torus

Overview

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, this classification is based on the dividing set on the boundary. In my research, I answered 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. To do this, I used a novel technique known as bypass induction, in which I showed that bypass attachments could be used to simplify the dividing set. This allowed me to obtain and solve a recurrence relation. Previously, the only fully classified 3-manifold was the 3-ball, and only a few special cases on the solid torus were known by Honda (2000).

Awards (2)

• Second Award of $2,000 $2,000
• American Mathematical Society: First Award of $2,000 $2,000

Competition history

• ISEF 2021 Mathematics · Entry MATH048

Resources

• ISEF abstract page ↗

Related projects

Closest projects by meaning, across every fair and year in the corpus.