Geodesic
On the Coincidence Points of Mappings of the Torus into a Surface
Informatics and Automation, Geometric topology and set theory, Tome 247 (2004), pp. 15-34

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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. 
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     author = {S. A. Bogatyi and E. A. Kudryavtseva and H. Zieschang},
     title = {On the {Coincidence} {Points} of {Mappings} of the {Torus} into a {Surface}},
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S. A. Bogatyi; E. A. Kudryavtseva; H. Zieschang. On the Coincidence Points of Mappings of the Torus into a Surface. Informatics and Automation, Geometric topology and set theory, Tome 247 (2004), pp. 15-34. http://geodesic.mathdoc.fr/item/TRSPY_2004_247_a2/