Does there exist a transformation between a loop and a close loop ?

[peter308]

Does there exist a transformation between a line and a closed loop ?

Dear All:
For a line structure(say a very long atomic chain) and a closed loop structure( connect the head and tail of this atomic chain). Does there exists a transformation between these two structures?
For example if we want to study the vibration mode of these two cases. If we already know all the modes of one case then are we able simultaneously know the information of the other modes without any further calculation?

Best Yen

 

[fresh_42]

Yes, but not a linear one. An example is the Riemann sphere: https://en.wikipedia.org/wiki/Riemann_sphere
The problem is the you can only map one pole, the other one is at infinity.