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How a local diffeomorphism preserves orientation

  1. Sep 30, 2012 #1
    Hi, I'm currently reading Manfredo do Carmo's "Differential Geometry of curves and surfaces" and I'm stocked with problem 2 of section 2-6 which is "Let [itex] S_2 [/itex] be an orientable regular surface and [itex] \varphi:S_1 \rightarrow S_2 [/itex] be a differentiable map which is a local diffeomorphism at every [itex]p \in S_1 [/itex].Prove that [itex] S_1 [/itex] is orientable".
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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