My reservations are related. There are tame knots and there are wild knots, and there are different notions of deformation and cancellation in the two respective settings. Before I believe Dan's (admittedly cute) argument I'll need to see an analysis that pays attention to this nicety. Jim On Thu, Oct 8, 2015 at 11:53 AM, Warren D Smith <warren.wds@gmail.com> wrote:
I'm worried about the validity of that proof.
The issue I have is that perhaps this would "prove" that unknot+unknot does not equal unknot?
See, if we had a finite sum of unknots, then they ought to be untangleable in a finite number of steps to make it obvious that the result is the unknot.
But it perhaps is not obvious that an infinite sum can thus be untangled.
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