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

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

2004-01-20

arxiv.org/abs/math/0401257v2

Contemporary Mathematics, Volume 389, 2005, p. 69 -89

Mathematics

Differential Geometry

26 pages, 9 figures

Scientific paper

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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