Geodesic
Intersection of loops in two-dimensional manifolds.~II. Free loops
Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 357-366

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In this paper the authors establish algebraic conditions necessary and sufficient for given free homotopy classes of loops in two-dimensional manifolds to be representable by simple nonintersecting loops. Bibliography: 9 titles. 
@article{SM_1984_49_2_a4,
     author = {V. G. Turaev and O. Ya. Viro},
     title = {Intersection of loops in two-dimensional {manifolds.~II.} {Free} loops},
     journal = {Sbornik. Mathematics},
     pages = {357--366},
     publisher = {mathdoc},
     volume = {49},
     number = {2},
     year = {1984},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1984_49_2_a4/}
}
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V. G. Turaev; O. Ya. Viro. Intersection of loops in two-dimensional manifolds.~II. Free loops. Sbornik. Mathematics, Tome 49 (1984) no. 2, pp. 357-366. http://geodesic.mathdoc.fr/item/SM_1984_49_2_a4/