# Classification of tight contact structures on surgeries on the figure-eight knot

## TL;DR

This paper classifies tight contact structures on surgeries of the figure-eight knot, identifying which are fillable and universally tight, thus advancing understanding in contact topology of hyperbolic 3-manifolds.

## Contribution

It provides the first classification of tight contact structures on an infinite family of hyperbolic 3-manifolds obtained via knot surgeries.

## Key findings

- Classified tight contact structures on surgeries of the figure-eight knot
- Identified which structures are symplectically fillable
- Determined which are universally tight

## Abstract

Two of the basic questions in contact topology are which manifolds admit tight contact structures, and on those that do, can we classify such structures. We present the first such classification on an infinite family of (mostly) hyperbolic 3-manifolds: surgeries on the figure-eight knot. We also determine which of the tight contact structures are symplectically fillable and which are universally tight.