Hi: I am trying to show that if we have a diffeomorphism f:M-->N and C is a positively-oriented Jordan curve in M ( so that., the winding number of C about any point in its interior is 1 ) , then f(C) is also positively-oriented in the same sense. It seems like something obvious to do is to use the fact that if F : M-->N is a diffeo. then F_* T_pM and T_pF(M) is a V.Space isomorphism. I imagine we can consider the curve (since it is a Jordan curve, I think reasonably-nice ) as embedded in M , and then we can see the tangent space of the curve as a subspace of T_pM , and so we have a vector space isomorphism G* T_qM -->T_F(q)M for q in the curve. Now, I think we can describe that a curve is positively-oriented by using a V.Field (which points towards the interior of C at each point, so that if we are walking along the curve, the interior will be to our left) , and the diffeo. inducing a V.Space isomorphism, at each point, should preserve this property, but I don't see how to make this more precise; I don't even know how to define a V.Field that describes positive orientation. Thanks For Any Ideas.