How to Describe the Riemann Surface Associated with a Complex Function?

[Petroz]

Hi guys,

My gf is doing honours and is having some trouble with one question on her assignment for complex analysis. She is really stuck and I've only done this topic at an undergraduate level so I have no idea. Neither of us have done any subjects in Topology so we don't know what to do.

She is required to describe the Riemann surface associated with a function
f(z) = sqrt( (z - x1)(z - x2)...(z - xn) )
where xi is an element of the real number set.
It comes with the hint: Consider n odd and even seperately.

If anyone could shed some light on this it would be greatly apprecicated.

Thanks for your time,

-Petroz

 

[mathwonk]

imagine a double cover of a sphere with n branch points.

e.g. if n=4 you get a torus.