# Identification question

1. Aug 10, 2007

### ehrenfest

What is the space resulting from the identification (x,y) ~ (x+2piR, y+2piR)? How is it different from the space resulting from
(x,y) ~ (x+2piR, y)
(x,y) ~ (x, y+2piR), which is a two-dimensional torus (a donut)

2. Aug 10, 2007

### f-h

It's a cylinder, rolled up along the diagonal.

3. Aug 10, 2007

### ehrenfest

What diagonal?

4. Aug 10, 2007

### CompuChip

I'd say the diagonal indicated on the attachment (up to symmetry :tongue:)

#### Attached Files:

• ###### diagonal.jpg
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Last edited: Aug 10, 2007
5. Aug 10, 2007

### ehrenfest

Sorry, I don't see any attachment. Was that just a joke?

6. Aug 10, 2007

### CompuChip

No, I forgot to click upload. Apparently you posted while I added it.

(BTW: Post $13^2$ for me)

7. Aug 10, 2007

### ehrenfest

$13^2$

Why would you ask me to post that?

8. Aug 10, 2007

### Staff: Mentor

He meant he hit post #169, he did not want you to post anything.

9. Aug 10, 2007

### f-h

Take (x,y) to (x+a,y+a) and you move up parallel to the diagonal between the x and the y axis. if you identify after a = 2Pi then you get a cylinder rolled along that diagonal.

10. Aug 10, 2007

### George Jones

Staff Emeritus
ehrenfest, what happens if you switch to coordinates x' = (x + y)/sqrt(2) and y' = (x - y)/sqrt(2)?

11. Aug 10, 2007

### ehrenfest

I see why it is different than the other identification! The R has to be the same for both x and y.

If you switch to light-cone coordinates, then it is a cylinder rolled around the y' axis, right?