Topology / complex analysis / what
Dec. 6th, 2016 10:50 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
jackFor 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 :)
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 :)