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Re: 4d-world [Was: Re: I'm back!]

From:Muke Tever <hotblack@...>
Date:Wednesday, September 22, 2004, 13:10
On Tue, 21 Sep 2004 20:46:41 -0700, Apollo Hogan <apollo@...> wrote:
> On Tue, 21 Sep 2004, H. S. Teoh wrote: > >> On Tue, Sep 21, 2004 at 03:37:43PM -0700, Apollo Hogan wrote: >> [...] >> >> Interesting, can you actually tie a sphere into a knot in 4D? I >> thought you could only do it to a 2D surface in 4D. But maybe I'm >> wrong. >Well, I meant S^2, the _skin_ or surface of a ball, not the solid ball. > (I.e. the unique-up-to-homeomorphism compact two-manifold without boundary > and with genus -2, :-) But I do think that you can tie it into a knot > in 4-space. You can also link together spheres (S^2) inseparably, just as we > can link rings inseparably in 3-space. >One way (not the only way) to generate knotted spheres in 4-space is to > "suspend" ordinary knots in 3-space... The idea is something like the knot > becomes the "equator" of the sphere... just take two hemispheres, sew them > together along the knot (of course you can't do this in 3-space, because of > the twisting of the knot, but there's room in 4-space). Voila, you've got > a knot. (Warning: I've not thought very much about this, so I'm bound to > say something wrong, but the idea is something like this.)
Is that like the one where you take a Möbius strip and close it by sewing a panel along the edge? *Muke! -- website: LiveJournal: deviantArt: FrathWiki, a conlang and conculture wiki:


Apollo Hogan <apollo@...>