The theorem below which states that is also called the monodromy theorem.
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This is called the "'monodromy theorem "'and its statement is made precise below.
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In complex analysis, the "'monodromy theorem "'is an important result about analytic continuation of a complex-analytic function to a larger set.
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The monodromy theorem makes it possible to extend an analytic function to a larger set via curves connecting a point in the original domain of the function to points in the larger set.
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The monodromy theorem gives sufficient conditions for analytic continuation to give the same value at a given point regardless of the curve used to get there, so that the resulting extended analytic function is well-defined and single-valued.
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Now I believe I can choose a'base point'somewhere in the surface constructed by the gluing and then use analytic continuation to extend this to any given point-I am also fairly sure that whatever path we choose to extend it, we should get the same end result presumably, because we need the map to be well-defined-I suspect this follows from the Monodromy theorem.
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