Topology / complex analysis / what

[jack]

For a plot bunny (yes, really :)):

You have a multivalued function from a sphere onto "some surface", continuous everywhere except two points. (Or, equivalently, a function from "some surface" to the sphere, I guess?)

If you look at points on the surface which map onto the same point on the sphere, and connections between them of "paths" on the sphere (up to continuous deformation), I feel like they end up acting like the integers, where "+1" and "-1" correspond to a clockwise of anticlockwise circumnavigation. Or possibly some subset, a cyclic group of some finite order, if there are repeats. Is that right?

If you have *three* points, what can the relationship between the points look like? What about more?

I remember doing something like that but not what it's called.

I'm trying to put something like the shadows of amber onto a more concrete mathematical footing :)

Comments

[jack]

:)

[simont]

(I vaguely recall someone telling me once, on that subject, that there's a text adventure game set on the interior of a Rubik's cube – the rooms are organised in a 3×3 grid and there are some puzzle actions you can take to perform face turns...)