We give a Thurston-like definition for laminations on higher Teichmüller spaces associated to a surface S and a semi-simple group G for G D SLm or PGLm. The case G D SL2 or PGL2 corresponds to the classical theory of laminations on a hyperbolic surface. Our construction involves positive configurations of points in the affine building. We show that these laminations are parametrized by the tropical points of the spaces XG;S and AG;S of Fock and Goncharov. Finally, we explain how the space of projective laminations gives a compactification of higher Teichmüller space.
ASJC Scopus subject areas
- Geometry and Topology