I know that this has been discussed several times, but I was not able to find a fully convincing conclusion. Suppose there are two twins travelling with relative velocity v on a torus. 1st question: is it possible to find one unique inertial frame which can serve as a global rest frame? my answers is "yes" b/c an observer can send out light signals in opposite direction; if and only if she receives these light signals at the same instant of time her rest frame is identical with this global rest frame. 2nd question: does a twin residing in this global rest frame observe time dilation for the second twin orbiting the torus with velocity v? my answer is "yes" b/c the travel of the second twin around the torus will take some time T = L/v where L is the spatial length of the circle (T, L and v measured in the global rest frame); so the proper time for the second twin will be T' < T (calculated via standard methods in the global rest frame). However, it seems to me that there is no general consensus regarding these two statements.