Discussion:
Simple identification problem
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Fausap
2005-06-26 10:49:47 UTC
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Hello all,

first of all, I'm sorry for the stupid question, but it's really
important to me to understand this thing :-)

I'm reading and studying the very nice book of Zwiebak and i'm working
on a quick calc about a plane identification:

(x,y) ~ (x+2piR, y+2piR)

This should identify the entire plane (x,y) with the other planes
(x+2piR, y+2piR) ... (x+4piR,y+4piR), etc.

I have no idea about the geometric view of this object... but I think
it shouldn't be a 3d obj.
Is it correct?

thanks in advance,
Fausto
Jeff L Jones
2005-06-27 07:25:40 UTC
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Post by Fausap
(x,y) ~ (x+2piR, y+2piR)
...
Post by Fausap
I have no idea about the geometric view of this object... but I think
it shouldn't be a 3d obj.
Is it correct?
Depends what you mean by 3d. This object is topologically a torus, but
geometrically it's flat. If you smoothly distorted it by giving it some
curvature in one direction, then you could visualize it as a geometrical
torus embedded in 3-dimensions. But the surface itself has only 2
dimensions since it's parametrized by 2 coordinates (x and y).
--
Jeff L Jones <***@spoonless.net>
Jeff L Jones
2005-06-27 07:25:51 UTC
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Post by Fausap
(x,y) ~ (x+2piR, y+2piR)
Regarding my previous message... which hasn't passed moderation yet.
I should not have said torus for this case, but cylinder. I was
thinking of:
(x,y) ~ (x+2piR,y)
(x,y) ~ (x,y+2piR)

which *would* be a torus since it has both edges identified rather
than just one.

Embedding the cylinder in 3 dimensions would be doable with no change in
geometry. (I'm currently trying to learn string theory as well, but so
far I've been mostly looking at Polchinski's book.) I hope if I've made
any further errors someone will correct me.
--
Jeff L Jones <***@spoonless.net>
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