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Torus/Z2
Posted:
Jun 30, 2011 5:45 AM


I can't find the answer to the following simple question:
In R^4 I have a torus T:
(x1)^2+(x2)^2=1 (x3)^2+(x4)^2=1
The group Z_2 acts on this torus via the reflection F(x)=x, x=(x1,x2,x3,x4)
What kind of a surface do we get by taking the quotient T/Z_2? Again torus? Sphere? Klein bottle? Something else? What would be the answer and to get it?
Thanks
P.S. For the standard torus in R^3 and another action of Z_2 the answer is in an example in do Carmo book on differential geometry of surfaces.



