[math-fun] Fwd: [xbbn] Graduate Student Solves Decades-Old Conway Knot Problem | Quanta Magazine
Some of us know Dick Koolish -- he posted the following link on the Bolt, Beranek & Newman alumni list. I wonder if Conway heard that his knot had been cracked -- the article came out in February. Also, it was refreshing to read an article that really captured the basic skeleton of an abstruse proof. I like Piccirilli's style. ---------- Forwarded message --------- From: Richard Koolish <koolish@dickkoolish.com> Date: Fri, May 22, 2020 at 6:39 PM Subject: [xbbn] Graduate Student Solves Decades-Old Conway Knot Problem | Quanta Magazine To: <xbbn@googlegroups.com> https://www.quantamagazine.org/graduate-student-solves-decades-old-conway-kn... -- You received this message because you are subscribed to the Google Groups "xBBN" group. To unsubscribe from this group and stop receiving emails from it, send an email to xbbn+unsubscribe@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/xbbn/6A36C8F2-51CA-4F7D-972B-3CEFEC758F3C%... .
The preprint has been up since Aug. 2018, and the Conway knot is also mentioned in her dissertation from May 2019. So maybe Conway did see. I was wondering if Chaim saw it, since he was also advised by Leucke, and probably would have liked to find this proof himself. I looked at some the work last week, and thought that the drawings were very well done. Other than Jargon, the writing also seemed good. Since I am not an expert on knot theory, I don’t know if the proof is right or not (but I assume that it is). Her dissertation is also not helpful to an outsider. This is pretty typical of the academic system, which actively encourages researchers to leave most people behind. When it comes to style, I usually prefer “here’s how you can catch up” to “here’s how we have gotten ahead”, but I’m sure part of that is regional bias. Given that Piccirillo’s (with an o at the end) style is very minimal, what other resources are helpful on the learning curve to proving the result? —Brad
On May 23, 2020, at 6:55 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Some of us know Dick Koolish -- he posted the following link on the Bolt, Beranek & Newman alumni list. I wonder if Conway heard that his knot had been cracked -- the article came out in February. Also, it was refreshing to read an article that really captured the basic skeleton of an abstruse proof. I like Piccirilli's style.
---------- Forwarded message --------- From: Richard Koolish <koolish@dickkoolish.com> Date: Fri, May 22, 2020 at 6:39 PM Subject: [xbbn] Graduate Student Solves Decades-Old Conway Knot Problem | Quanta Magazine To: <xbbn@googlegroups.com>
https://www.quantamagazine.org/graduate-student-solves-decades-old-conway-kn...
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This is great. But I have a question. I had the impression that d-dimensional surfaces can be “knotted” (homeomorphic but not homotopic to a sphere, if I’m remembering the correct uses of those lovely greek-derived words) in 2d+1 dimensions: 1-dimensional curves in 3 dimensions, 2-dimensional surfaces in 5, and so on. But this artlcle says that 2-dimensional surfaces can be knotted in 4 dimensions. I can see how two spheres (2-dimensional surfaces) can be linked in 5 dimensions: put them in 3 dimensions so that the overlap and intersect in a circle, and then “lift” each point on that circle to a pair of antipodal points on a circle in another 2 dimensions. Then the two spheres cannot be drawn apart without having them intersect in all 5 dimensions at some point. But I don’t see a similar construction in 4 dimensions. Can anyone give a simple example of a knot or link of 2-surfaces in 4 dimensions? Cris
On May 23, 2020, at 5:55 PM, Allan Wechsler <acwacw@gmail.com> wrote:
Some of us know Dick Koolish -- he posted the following link on the Bolt, Beranek & Newman alumni list. I wonder if Conway heard that his knot had been cracked -- the article came out in February. Also, it was refreshing to read an article that really captured the basic skeleton of an abstruse proof. I like Piccirilli's style.
---------- Forwarded message --------- From: Richard Koolish <koolish@dickkoolish.com> Date: Fri, May 22, 2020 at 6:39 PM Subject: [xbbn] Graduate Student Solves Decades-Old Conway Knot Problem | Quanta Magazine To: <xbbn@googlegroups.com>
https://www.quantamagazine.org/graduate-student-solves-decades-old-conway-kn...
-- You received this message because you are subscribed to the Google Groups "xBBN" group. To unsubscribe from this group and stop receiving emails from it, send an email to xbbn+unsubscribe@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/xbbn/6A36C8F2-51CA-4F7D-972B-3CEFEC758F3C%... . _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
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Allan Wechsler -
Brad Klee -
Cris Moore