Re: Looking for a surjection or R^2

I wrote:

....
As before, identify R^2 with C, and let p(z)=z^3-3z. Then p is a
3-sheeted irregular branched cover of C over C, with critical points
1 and -1, and critical values -2 = p(1) = p(-2) and 2 = p(-1) = p(2).
The preimage p^{-1}(R), call it G, is the union of R and two (real)
parabolas

which is of course wrong--with z = x+iy as usual, G is the zero-set
of y(3x^2-y^2-1), so it's the union of R and the two branches of a
*hyperbola*.

Lee Rudolph


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