Re: Euler characteristic of torus

James wrote: (with hardly a *single* carriage return)


I know a covering of the torus is R x R. I know a
theorem that if X ----> Y is a finite covering (k sheets)
and Y is a finite CW complex, then Euler(X) = k*Euler(Y)
where Euler(X) denotes Euler characteristic of X.
But R x R isn't a finite covering of the torus (and it
isn't even a finite CW complex, right?) So I can't use
R x R as the cover to compute Euler(torus). What other
covering spaces are there of the torus?

Can you see how to make the torus a double cover of
itself?
.

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