| Résume | The skein algebra of a topological surface is constructed from knots and links in the 3-manifold obtained by taking the product of the surface with an interval. A conjecture of Dylan Thurston predicts the positivity of the structure constants of a certain linear basis of the skein algebra. I will explain a recent proof of this conjecture for the skein algebra of the 4-punctured sphere. In a slightly surprising way, this proof of a topological result relies on complex algebraic geometry and in particular the study of algebraic curves in complex cubic surfaces. |
