Zwiebach's A First Course in String Theory
Quick Calculation 2.5: Consider the plane (x,y) with the identification
[tex](x,y)\rightarrow (x+2\pi R,y+2\pi R)[/tex].
What is the resulting space?
A one dimensional line with identification [tex]x\rightarrow x+2\pi R[/tex] is a circle.
A plane with identifications
[tex](x,y)\rightarrow (x+2\pi R,y)[/tex]
[tex](x,y)\rightarrow (x,y+2\pi R)[/tex]
is a torus.
The Attempt at a Solution
The identification is just the combination of both of the torus identifications... but how would I join two boundaries with a single identification? And what would be the fundamental domain? Thanks!