Riemann Surfaces

  • Hershel M. Farkas
  • Irwin Kra
Part of the Graduate Texts in Mathematics book series (GTM, volume 71)


In this chapter we define and give the simplest examples of Riemann surfaces. We derive some basic properties of Riemann surfaces and of holomorphic maps between compact surfaces. We assume the reader is familiar with the elementary concepts in algebraic-topology and differential-geometry needed for the study of Riemann surfaces. To establish notation, these concepts are reviewed. The necessary surface topology is discussed. In later chapters we will show how the complex structure can help obtain many of the needed results about surface topology. The chapter ends with a development of various integration formulae.


Normal Form Riemann Surface Holomorphic Mapping Meromorphic Function Fundamental Group 
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Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • Hershel M. Farkas
    • 1
  • Irwin Kra
    • 2
  1. 1.Department of MathematicsThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Department of MathematicsS.U.N.Y. at Stony BrookStony BrookUSA

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