Degrees, Intersection Numbers, and the Euler Characteristic
We now have enough machinery at our disposal to develop one of the most important tools in topology: the degree of a map f: M → N, 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.
KeywordsVector Field Euler Characteristic Intersection Number Normal Bundle Homotopy Class
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