Computing the Euler Characteristic

  • Arlie O. Petters
  • Harold Levine
  • Joachim Wambsganss
Part of the Progress in Mathematical Physics book series (PMP, volume 21)


One of the most important numerical invariants in mathematics is the Euler characteristic. We shall investigate the Euler characteristic of a surface in terms of the critical points of maps from the surface into the plane. This material will be applied later to the study of the global geometry of caustics (see Section 15.4.2).


Normal Form Euler Characteristic Rotation Number Morse Function Orientation Preserve 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Arlie O. Petters
    • 1
  • Harold Levine
    • 2
  • Joachim Wambsganss
    • 3
  1. 1.Department of MathematicsDuke UniversityDurhamUSA
  2. 2.Department of MathematicsBrandeis UniversityWalthamUSA
  3. 3.Astrophysikalisches Institut PotsdamUniversität PotsdamPotsdamGermany

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