Geodesic
On non-separating simple closed curves in a compact surface
Electronic research announcements of the American Mathematical Society, Tome 01 (1995) no. 1, pp. 18-25.

Voir la notice de l'article provenant de la source American Mathematical Society

We introduce a semi-algebraic structure on the set $\mathcal {S}$ of all isotopy classes of non-separating simple closed curves in any compact oriented surface and show that the structure is finitely generated. As a consequence, we produce a natural finite dimensional linear representation of the mapping class group of the surface. Applications to the Teichmüller space, Thurston’s measured lamination space, the harmonic Beltrami differentials, and the first cohomology group of the surface are discussed. 
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Luo, Feng. On non-separating simple closed curves in a compact surface. Electronic research announcements of the American Mathematical Society, Tome 01 (1995) no. 1, pp. 18-25. doi : 10.1090/S1079-6762-95-01003-1. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-95-01003-1/

[1] Dehn, Max Papers on group theory and topology 1987

[2] Travaux de Thurston sur les surfaces 1979 284

[3] Lickorish, W. B. R. A representation of orientable combinatorial 3-manifolds Ann. of Math. (2) 1962 531 540

[4] Humphries, Stephen P. Generators for the mapping class group 1979 44 47

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