Hi: This problem should be relatively simple, but I have been going in circles, without figuring out a solution: If f:X->R^2k is an immersion and a is a regular value for the differential map F_*: T(X) -> R^2k, where F(x,v) = df_x(v). Then show F^-1 (a) is a finite set. I have tried using the differential topology def. of degree of a map , where we calculate the degree by substracting the number of points where the Jacobian has negative determinant (orientation-reversing) minus the values where JF has positive determinant. I think I am close, but not there. Any Ideas? Thanks.