• Morris W. Hirsch
Part of the Graduate Texts in Mathematics book series (GTM, volume 33)


A surface is a two-dimensional manifold. The classification of compact surfaces was “known,” in some sense, by the end of the nineteenth century. Möbius [1] and Jordan [1] offered proofs (for orientable surfaces in ℝ3) in the 1860’s. Möbius’ paper is quite interesting; in fact he used a Morse-theoretic approach similar to the one presented in this chapter. The main interest in Jordan’s attempt is in showing how the work of an outstanding mathematician can appear nonsensical a century later.


Boundary Component Euler Characteristic Compact Surface Morse Function Klein Bottle 
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Copyright information

© Springer-Verlag New York Inc. 1976

Authors and Affiliations

  • Morris W. Hirsch
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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