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Surfaces

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

Abstract

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.

Keywords

Boundary Component Euler Characteristic Compact Surface Morse Function Klein Bottle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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