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Math Help - vector field on surface

  1. #1
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    vector field on surface

    The question is :
    Prove that an orientable compact surface in R^3 has a differentiable vector field without singular points iff S is homeomorphic to a torus

    I have proved one direction by using Poincare's theorem ,but I can't prove that if S is homemorphic to a torus then it has a vector field without singular points,please help.
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  2. #2
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    If the torus is obtained from the unit square by identifying opposite edges, then you can use any constant (nonzero) vector field on the square.
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