Abstract
Shortly after Cauchy and Puiseux, Riemann came up with a radically different solution to the problem of multivaluedness of functions.
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Notes
- 1.
In the next fragment, x and y denote the real and imaginary parts of the variable \(z \in \mathbb{C}\).
- 2.
I took the picture from [172, page 284].
- 3.
In Chap. 40 we will see how one arrived, historically speaking, at this mode of expression.
- 4.
In this text, x and y again denote the real and imaginary parts of a complex variable z, which is a local complex coordinate on the surface T.
- 5.
Note that here, in contrast to the situation considered in the Introduction, the loops are allowed to intersect.
- 6.
See Theorem 41.1 for its general modern statement. Here, in the context of curvilinear integrals on surfaces, it is often called the Green–Riemann formula.
- 7.
The translation into English was done by Weil.
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Popescu-Pampu, P. (2016). Riemann and the Cutting of Surfaces. In: What is the Genus?. Lecture Notes in Mathematics(), vol 2162. Springer, Cham. https://doi.org/10.1007/978-3-319-42312-8_14
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