On the Coincidence Points of Mappings of the Torus into a Surface

For an arbitrary pair of continuous maps of the $2$-torus $T$ into an arbitrary surface $S$, the Wecken property for the coincidence problem is proved. This means that there exist homotopic maps such that each Nielsen class of coincidence points consists of a single point and has a nonvanishing index. Moreover, every nonvanishing index is equal to $\pm 1$, as well as every nonvanishing semi-index of Jezierski is equal to $1$ if $S$ is neither the sphere nor the projective plane.