  We consider the gathering problem for asynchronous and oblivious robots that
cannot communicate explicitly with each other, but are endowed with visibility
sensors that allow them to see the positions of the other robots. Most of the
investigations on the gathering problem on the discrete universe are done on
ring shaped networks due to the number of symmetric configuration. We extend in
this paper the study of the gathering problem on torus shaped networks assuming
robots endowed with local weak multiplicity detection. That is, robots cannot
make the difference between nodes occupied by only one robot from those
occupied by more than one robots unless it is their current node. As a
consequence, solutions based on creating a single multiplicity node as a
landmark for the gathering cannot be used. We present in this paper a
deterministic algorithm that solves the gathering problem starting from any
rigid configuration on an asymmetric unoriented torus shaped network.
