Gluing Affine 2-Manifolds with Polygons |
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Authors: | Oliver Baues |
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Affiliation: | (1) Department of Mathematics, ETHZ, CH-8092 Züurich, Switzerland |
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Abstract: | Affine structures on surfaces are constructed by gluing polygons. The geometry of the affine surface depends on the shape of the polygon(s) and the particular gluing transformations used. The affine version of the Poincaré fundamental polygon theorem expresses the fundamental group and holonomy of the surface in terms of the gluing data. The theorem may be used to construct all complete affine structures on the 2-torus. The space of inequivalent holonomy representations of such structures is homeomorphic to R2. |
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Keywords: | affine structure 2-manifolds complete affine surface poincaré fundamental polygon shape of polygons deformation space moduli space. |
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