Complex Analysis and Surface Topology

  • John Stillwell
Part of the Graduate Texts in Mathematics book series (GTM, volume 72)


Topology may have had its tentative beginnings in isolated thoughts of Descartes, Leibniz, and Euler, but it was Riemann who brought the subject into the mainstream of mathematics with his inaugural dissertation in Göttingen in 1851. His introduction of the Riemann surface in that year showed the indispensable rôle of topology in questions of analysis, and thus ensured the future cultivation of the subject by the mathematical community, if only for the service of analysis. In fact, of course, Riemann surfaces were quickly seen to be of interest in themselves, and were the source of two ideas of profound significance in later topology—connectivity and covering spaces.


Riemann Surface Branch Point Euler Characteristic Fuchsian Group Surface Topology 
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Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • John Stillwell
    • 1
  1. 1.Department of MathematicsMonash UniversityClaytonAustralia

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