2
$\begingroup$

I study the function $z\to \dfrac{z^3}{z^4+27}$. The branch points are $z=-3i,-3,0,3,3i$. I have $4$ copies of the sphere (degree of the rational function). And I calculate the monodromy group to know the permutation and determinate the copies that coincide in the branch points. See the figure. Copies of sphere that coincide in the branch points

my question is How i do made the cuts and glue for the copies? I try the planar representation of the Sphere. But i don´t now if this is correct. I cut from the lines and make a identification to glue the copies. Planar representation

Please Help, sorry for my English

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.