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Title:
Constructing Riemann surfaces from equilateral triangles
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Abstract:
We consider the following question. Suppose that a (finite or infinite) collection of equilateral triangles are glued together in such a way that each edge is identified with precisely one other edge, and each vertex is identified with only finitely many other vertices. If the resulting surface is connected and orientable, it naturally has the structure of a Riemann surface, i.e., a one-dimensional complex manifold. We ask which surfaces can arise in this fashion.
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