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Is the deformation space of complete affine structures on the 2-torus smooth?

Oliver Baues·William M. Goldman
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Abstract

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 structure on this deformation space, under which it is diffeomorphic to $R^2$. The action of the mapping class group of $T^2$ is equivalent in these coordinates with the standard linear action of $\SL_2(Z)$ on $R^2$.

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Oliver Baues, William M. Goldman. 2005-06-14. Is the deformation space of complete affine structures on the 2-torus smooth?. https://arxiv.org/abs/math/0401257

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