Question about closing a chain of elastic bands -- and hatching eggs

[Timothy Y. Chow]

Alex Galicki wrote:
> However, if we say that "ring" means the end result of the procedure you 
> have described ("if the last band added is cut before the chain is 
> closed and the cut repaired afterwards"), then such a ring always 
> contains a Hopf link.

Perhaps Aaron should clarify, but this doesn't sound right to me.  When 
you cut and repair, what you want to end up with is something that looks 
like the picture shown here:

https://i.ytimg.com/vi/gntXhYfunC4/maxresdefault.jpg

That's not a Hopf link.  Another way to see it is, in Aaron's 
configuration, if you delete any single rubber band, then the whole thing 
comes apart (a "Brunnian link").  So if there are at least three rubber 
bands, then there cannot be a Hopf link---choose a rubber band not 
involved in the Hopf link and delete it, and the Hopf link remains linked.

Googling around, I found this page, which seems to indicate that the Jones 
polynomial suffices to distinguish it from an unlink:

http://katlas.math.toronto.edu/wiki/%22Rubberband%22_Brunnian_Links

Tim