Timeline for Can infinity shorten proofs a lot?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 19, 2012 at 20:12 | comment | added | André Henriques | The argument shows that if A has a connected sum-inverse, then it is isotopic to the unknot by some continuous isotopy. I would like to know that if A has a connected sum inverse, then it is isotopic to the unknot by some smooth isotopy. Is there a variation of the argument that shows that? | |
| Feb 15, 2012 at 17:44 | history | edited | David White | CC BY-SA 3.0 |
Texified
|
| Nov 17, 2009 at 21:07 | comment | added | Scott Carter | Yes, and according to the wikipedia link above, it is used in Rolfsen to give the proof that I indicated. | |
| Nov 17, 2009 at 6:08 | comment | added | Ryan Budney | The Mazur swindle is so good it gets 1st and 2nd place. :) | |
| Nov 17, 2009 at 4:11 | comment | added | Harrison Brown | This is essentially the Mazur swindle, right? | |
| Nov 17, 2009 at 3:36 | comment | added | Ryan Budney | Another spin on this is that all tame knots in co-dimension larger than two are topologically trivial. So if you apply this argument to Haefliger's non-trivial smooth knots (S^3 in S^6, say -- and these do have inverses in the smooth category) you see a "nice" example of how the topological and smooth category differ. | |
| Nov 17, 2009 at 3:23 | history | answered | Scott Carter | CC BY-SA 2.5 |