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Riemann Surfaces

In: Differential and Complex Geometry: Origins, Abstractions and Embeddings

Author

Listed:
  • Raymond O. Wells Jr.

    (University of Colorado Boulder
    Jacobs University Bremen)

Abstract

The work of Abel on Abelian integrals created a particular theory of multivalued transcendental functions on the complex plane. This was a primary motivation for Riemann to create his theory of Riemann surfaces in 1857, which were multisheeted coverings of the complex plane where these functions of Abel (and other such functions) would become singlevalued functions. Riemann developed some of the important concepts of connectivity for these surfaces, which became part of the developments in algebraic topology of manifolds in general at the end of the century.

Suggested Citation

  • Raymond O. Wells Jr., 2017. "Riemann Surfaces," Springer Books, in: Differential and Complex Geometry: Origins, Abstractions and Embeddings, chapter 0, pages 137-158, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-58184-2_10
    DOI: 10.1007/978-3-319-58184-2_10
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