Cluster structures on laminated Teichmüller spaces

Sergey Fomin

We construct a topological model for an arbitrary cluster algebra of geometric type whose exchange matrix can be interpreted as a signed adjacency matrix of a triangulated bordered surface. In this model, the coefficients come from a choice of a system of laminations on a surface, and cluster variables are represented by certain functions (generalized lambda lengths) on the corresponding "laminated Teichmüller space."

This is joint work with Dylan Thurston.