Degrees, Intersection Numbers, and the Euler Characteristic

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


We now have enough machinery at our disposal to develop one of the most important tools in topology: the degree of a map f: MN, where M and N are compact n-manifolds, N is connected, and ∂M = ∂N = Ø. This degree is an integer if M and N are oriented, an integer mod 2 otherwise.


Vector Field Euler Characteristic Intersection Number Normal Bundle Homotopy Class 


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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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