124 citations · 290 across the 37 of their papers we have counts for
5 papers · 1 filter
Proper affine actions and geodesic flows of hyperbolic surfaces
William Goldman, Francois Labourie, Gregory Margulis
We give necessary and sufficient conditions for an affine deformation of a Schottky subgroup of O(2,1) to act properly on affine space. There exists a real-valued biaffine map betw…
Homological action of the modular group on some cubic moduli spaces
William M. Goldman, Walter D. Neumann
We describe the action of the automorphism group of the complex cubic x^2+y^2+z^2-xyz-2 on the homology of its fibers. This action includes the action of the mapping class group of…
Rank One Higgs Bundles and Representations of Fundamental Groups of Riemann Surfaces
William M. Goldman, Eugene Z. Xia
This expository paper details the theory of rank one Higgs bundles over a closed Riemann surface X and their relationship to representations of the fundamental group of X. We const…
An exposition of results of Fricke
William M. Goldman
This paper gives an elementary proof of the result that the conjugacy classes of pairs (X,Y) of unimodular 2x2 complex matrices is an affine 3-space, parametrized by the traces of…
Is the deformation space of complete affine structures on the 2-torus smooth?
Oliver Baues, William M. Goldman
Periods of parallel exterior forms define natural coordinates on the deformation space of complete affine structures on the two-torus. These coordinates define a differentiable str…