Geodesic
Intersections of loops in two-dimensional manifolds
Sbornik. Mathematics, Tome 35 (1979) no. 2, pp. 229-250 Cet article a éte moissonné depuis la source Math-Net.Ru

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Given an arbitrary smooth two-dimensional manifold $A$ with nonempty boundary and a point $a\in\partial A$, mappings $\mathbf Z[\pi_1(A,a)]\times\mathbf Z[\pi_1(A,a)]\to\mathbf Z[\pi_1(A,a)]$ and $\pi_1(A,a)\to\mathbf Z[\pi_1(A,a)]$. are constructed. In terms of them the author formulates and proves necessary and sufficient conditions for realizability of an element of the group $\pi_1(A,a)$ by a simple loop, conditions for the realizability of a few elements of $\pi_1(A,a)$ by nonintersecting loops and conditions for realizability of an automorphism of this group by a diffeomorphism $(A,a)\to(A,a)$. Figures: 5. Bibliography: 14 titles. 
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     author = {V. G. Turaev},
     title = {Intersections of loops in two-dimensional manifolds},
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     volume = {35},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1979_35_2_a5/}
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V. G. Turaev. Intersections of loops in two-dimensional manifolds. Sbornik. Mathematics, Tome 35 (1979) no. 2, pp. 229-250. http://geodesic.mathdoc.fr/item/SM_1979_35_2_a5/

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