Hi:(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Regular values of immersion.

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