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Geometric structures on toroidal maps and elliptic curves. (English) Zbl 0984.05028
With every map on a surface there is an associated geometric structure (spherical, Euclidean, or hyperbolic) on the surface. A surface of genus \(>1\) always carries a hyperbolic structure, but the structure on a torus can be either Euclidean or hyperbolic. The authors study the toroidal maps which have a Euclidean structure, both from the viewpoint of graph embeddings and of elliptic curves.

05C10 Planar graphs; geometric and topological aspects of graph theory
57M15 Relations of low-dimensional topology with graph theory
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