This material is surely elementary, but I couldn't find it anywhere: maybe someone can cite a reference? A 2-sheet Riemann sphere with 2 winding points is homeomorphic to a torus: for if its tube radius remains fixed while the swept radius approaches zero, the torus approaches a double sphere with winding points at opposite ends of a diameter --- whence they may be deformed to arbitrary locations, and the sphere to a topological sphere. In a similar fashion, s sheets with t winding points are homeomorphic to a sphere with (s t)/4 handles, ie. genus = (s t)/4 , at any rate for s, t even; otherwise it perhaps suffices to take the ceiling ... I would probably have remained unaware of this idea if I had not once been experimenting with a simple Maple graphics demo program to plot a torus, and noticed that what I had casually assumed must be a simple sphere instead appeared mysteriously fuzzy and uneven. On this occasion at any rate, Maple was innocent of blame, and indeed had provided valuable insight! Fred Lunnon