Timeline for Blackbox Theorems
Current License: CC BY-SA 3.0
5 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jun 19, 2012 at 7:36 | comment | added | Daniel Moskovich | @Greg Kuperberg: I'm uneasy about my Frechet manifold intuition, so e.g. playing with Thom-Boardman stratification or multijet transversality looks hard to me right now (presentation of the MCG is also difficult). Maybe one day I'll feel more comfortable with it; maybe all topologists should (is there a nice intro text?). Anyway, these aren't standard things which "consumers" of Kirby's Theorem know much about. Reidemeister's Theorem's proof is at least combinatorial (a smooth proof uses weaker tools). What's the algebraic geometry proof of Thom transversality? I'm really curious about that! | |
| Jun 19, 2012 at 6:11 | comment | added | Greg Kuperberg | I confess that I have no looked at the proof of the Kirby calculus theorem either recently. But I personally think that the difficulty of the Thom transversality theorem and Cerf theory are overplayed. Is the Reidemeister move theorem for smooth knots a difficult theorem? It's the same sort of thing. Yes, there are a lot of details if you want to be very rigorous, but the lemmas all have natural statements. For instance, you can prove Thom transversality in the setting of a finite-dimensional vector space of polynomial functions, using algebraic geometry. | |
| Jun 14, 2012 at 17:20 | comment | added | Ian Agol | Freedman's theorem "Casson handles are handles" is also used as a black box by many people. Once this is known, standard arguments from higher dimensions can be pushed down to 4 dimensions to prove h-cobordism and Poincare. Hopefully this will be rectified next summer when an extended workshop will go over the proof (I think at Bonn). | |
| Jun 14, 2012 at 1:26 | history | answered | Daniel Moskovich | CC BY-SA 3.0 |