Timeline for answer to What are some correct results discovered with incorrect (or no) proofs? by Daniel Asimov
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| Apr 4, 2011 at 13:24 | history | made wiki | Post Made Community Wiki | ||
| Jul 9, 2010 at 9:47 | comment | added | Gunnar Þór Magnússon | I heard Smale tell a version of this story at the Clay conference in Paris a couple of months ago. He got interested in the Poincaré conjecture and spent a night coming up with a simple proof. The next morning he went to his advisor and explained the details, and all the time his advisor just sat there silent and nodded from time to time. Smale left the meeting a little frustrated that his proof hadn't been met with more interest, until he realized later that day that he had never used the hypothesis of simple connectedness. But yeah, he did say that this helped him in the proof for n>=5. | |
| Jun 12, 2010 at 0:34 | comment | added | Daniel Asimov | (cont'd) This can be achieved by starting with the canonical flow on S<sup>2</sup> x [0,1] (i.e., the one parallel to [0,1]) and introducing a "plug" -- a copy of S<sup>1</sup> x [0,1] x[0,1] -- on which the flow is altered. See, for instance, Plugging Flows by Percell and Wilson. For those with access, at < jstor.org/stable/pdfplus/1997824.pdf >. | |
| Jun 12, 2010 at 0:30 | comment | added | Daniel Asimov | Sure. The sentence starting with "Clearly" isn't. In fact there exist orientable 1-foliations (which result from C<sup>1</sup> nonsingular vector fields as the solutions to the corresponding ODE) on even S<sup>2</sup> x [0,1] that are entering on one boundary component and exiting on the other, without every trajectory that enters on one boundary component exiting on the other one. | |
| Jun 11, 2010 at 21:24 | comment | added | Tom LaGatta | Daniel, could you please explain the error in the reasoning? | |
| Jun 11, 2010 at 21:01 | history | answered | Daniel Asimov | CC BY-SA 2.5 |