Thin-shell toroidal wormhole

We consider a topologically nontrivial thin-shell wormhole with a throat in the form of a $T^2$ torus. It is shown that: (i)~such a wormhole is stable with respect to excitations of the throat; (ii)~not all energy conditions are violated for such wormholes; (iii)~if any of the energy conditions is violated, this violation occurs only partially in some region near the throat, and in other regions the violation is absent. Also, we discuss the differences between spherical $S^2$ wormholes and toroidal $T^2$ wormholes under investigation.