Spectral Radius Compactification of Hitchin Components

The spectral radius compactification is the generalization of Thurston’s compactification of Teichmüller space to SL(n,R) Hitchin components obtained by using logarithms of top eigenvalues in place of hyperbolic lengths. Just as Thurston boundary points parametrize R-trees, which are dual to measured laminations, we find that spectral radius boundary points parametrize n-1 dimensional polyhedral spaces which are dual to geodesic currents with particular restrictions on self intersection. The construction is particularly nice for n=3 where often the geodesic current comes in a concrete way from a cubic differential, and the polyhedral space is simply the universal cover of S equipped with a triangular Finsler metric.