Timeline for Independent evidence for the classification of topological 4-manifolds?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 15, 2021 at 19:34 | history | edited | Timothy Chow | CC BY-SA 4.0 |
Added excerpts from the book
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| Sep 17, 2021 at 16:14 | history | edited | Emilio Pisanty | CC BY-SA 4.0 |
deleted 26 characters in body
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| Sep 12, 2021 at 17:43 | comment | added | Gabe K | @none I don't fully understand the details of Perelman's proof, but it is more well understood than Friedman's work. Part of this is that people have spent a lot of time writing expositions of the proof. Also, the overarching strategy of the proof is fairly clear and once you see the monotonicity of the $\mathcal{W}$ functional and why it implies non-collapsing, the approach seems promising. There are many tough details along the way (e.g., ruling out the cigar soliton or showing that surgeries don't accumulate), but these are concrete steps which can be checked by experts. | |
| Sep 10, 2021 at 2:07 | comment | added | none | Came here because of the Quanta article, which indicates that Freedman's 4 dimensional proof is maybe even harder than Perelman's 3 dimensional proof. Can it really be like that? I read over Terence Tao's article about Perelman's proof and didn't understand it, but it gave a constant sense of having to spot and control issues that were very hard to visualize. I'd have no idea how to check such a proof even if I had the technical background. It seems too easy to miss something. | |
| Sep 9, 2021 at 18:28 | comment | added | Yemon Choi | @JasonRute With a reference to remarks in mathoverflow.net/a/117144 :) | |
| Sep 9, 2021 at 18:01 | comment | added | Jason Rute | Quanta magazine just published an article about this book: New Math Book Rescues Landmark Topology Proof | |
| May 26, 2021 at 18:45 | history | edited | Peter LeFanu Lumsdaine | CC BY-SA 4.0 |
Added title+details of book to text (more human-readable; and url-only references usually rot sooner or later)
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| May 26, 2021 at 17:44 | history | answered | Jens Reinhold | CC BY-SA 4.0 |