A <Riemann surface> is a Hausdorff, second-countable, one-dimensional <complex manifold>, with charts to <open subsets> of $\mathbb C$ whose transition maps are <holomorphic>. Connectedness is often included in the convention. A map between <Riemann surfaces> is <holomorphic> when its expression in every compatible pair of charts is <holomorphic>. It is <biholomorphic> when it is bijective and both it and its inverse are <holomorphic>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2006 / ii / Paper 2 / 23F / Solution

 Solution (source code)