general relativity - Symmetrical twin paradox in a closed universe

Take the following gedankenexperiment in which two astronauts meet each other again and again in a perfectly symmetrical setting - a hyperspherical (3-manifold) universe in which the 3 dimensions are curved into the 4. dimension so that they can travel without acceleration in straight opposite directions and yet meet each other time after time.

On the one hand this situation is perfectly symmetrical - even in terms of homotopy and winding number. On the other hand the Lorentz invariance should break down according to GRT, so that one frame is preferred - but which one?

So the question is: Who will be older? And why?

And even if there is one prefered inertial frame - the frame of the other astronaut should be identical with respect to all relevant parameters so that both get older at the same rate. Which again seems to be a violation of SRT in which the other twin seems to be getting older faster/slower...

How should one find out what the preferred frame is when everything is symmetrical - even in terms of GRT?

And if we are back to a situation with a preferred frame: what is the difference to the classical Galilean transform? Don't we get all the problems back that seemed to be solved by RT - e.g. the speed limit of light, because if there was a preferred frame you should be allowed to classically add velocities and therefore also get speeds bigger than c ?!? (I know SRT is only a local theory but I don't understand why the global preferred frame should not 'override' the local one).

Could anyone please enlighten me (please in a not too technical way because otherwise I wouldn't understand!)

EDIT
Because there are still things that are unclear to me I posted a follow-up question: Here

Answer

Your question is addressed in the following paper:

The twin paradox in compact spaces

Authors: John D. Barrow, Janna Levin
Phys. Rev. A 63 no. 4, (2001) 044104
arXiv:gr-qc/0101014

Abstract: Twins travelling at constant relative velocity will each see the other's time dilate leading to the apparent paradox that each twin believes the other ages more slowly. In a finite space, the twins can both be on inertial, periodic orbits so that they have the opportunity to compare their ages when their paths cross. As we show, they will agree on their respective ages and avoid the paradox. The resolution relies on the selection of a preferred frame singled out by the topology of the space.