The Euler Tour of $n$-Dimensional Manifold with Positive Genus

In the paper [1] it is proved that abstract cubic $n$-dimensional torus [2] possesses a directed Euler tour of the same dimension. The result prompts to a new (virtual) device for transmission and reception of information. In the present paper it is shown that every abstract cubic $n$-dimensional manifold without borders, of positive genus possesses a $n$-dimensional directed Euler tour. This result has practical application.