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