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

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!
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