Linking and Unlinking a Double Torus.
March 12, 2011
I cannot find a suitable picture of a linked double torus, which makes me think it’s called something else. Luckily, because it’s on the cover of Armstrong’s book (and I don’t think Springer would mind some free advertising) we can reproduce it here:
Now, how can we take this "linked" double torus and make it an "unlinked" double torus without cutting anything up? This one kept me up last night, but the solution turns out to be quite easy once you see it.
If you don’t want the full solution, a hint might be: start thinking of the double torus as two handles on a sphere. What can you do with these handles?
The picture solution after the jump.
Click to make this bigger.