We give a Thurston-like definition for laminations on higher Teichmuller spaces associated to a surface S and a semi-simple group G for G = SLm or PGL(m). The case G = SL2 or PGL(2) 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 X-G,X- S and A(G, S) of Fock and Goncharov. Finally, we explain how the space of projective laminations gives a compactification of higher Teichmuller space.
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机译：对于与表面S相关联的较高Teichmuller空间和G = SLm或PGL（m）的半简单群G，我们给出了类似于Thurston的定义。 G = SL2或PGL（2）的情况对应于双曲线表面上的经典叠层理论。我们的构造涉及仿射建筑物中各个点的正构形。我们表明，这些叠片是由Fock和Goncharov的空间X-G，X-S和A（G，S）的热带点参数化的。最后，我们解释了射影叠片的空间如何压缩更高的Teichmuller空间。
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