Riemann surface

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In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed versions of the complex plane: locally near every point they look like patches of the complex plane, but the global topology can be quite different. For example, they can look like a sphere or a torus or several sheets glued together. Examples of Riemann surfaces include graphs of multivalued functions such as z {\displaystyle {\sqrt {z}}} or log ⁡ ( z ) {\displaystyle \log(z)} , e.g. the subset of pairs ( z , w ) ∈ C 2 {\displaystyle...

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