Geodesic
Normal closures of powers of Dehn twists in mapping class groups
Glasgow mathematical journal, Tome 34 (1992) no. 3, pp. 314-317

Voir la notice de l'article provenant de la source Cambridge University Press

Let F = F(g, n) be an oriented surface of genus g≥1 with n<2 boundary components and let M(F) be its mapping class group. Then M(F) is generated by Dehn twists about a finite number of non-bounding simple closed curves in F([6, 5]). See [1] for the definition of a Dehn twist. Let e be a non-bounding simple closed curve in F and let E denote the isotopy class of the Dehn twist about e. Let Nbe the normal closure of E2in M(F). In this paper we answer a question of Birman [1, Qu 28 page 219]:Theorem 1. The subgroup N is of finite index in M(F). 
Humphries, Stephen P. Normal closures of powers of Dehn twists in mapping class groups. Glasgow mathematical journal, Tome 34 (1992) no. 3, pp. 314-317. doi: 10.1017/S0017089500008879
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[1] 1.Birman, J., Braids, links and mapping class groups, (Princeton University Press, Annals of Math Studies #82, 1975). Google Scholar | DOI

[2] 2.Jones, V., Hecke algebra representations of braid groups and link polynomials, Ann. Math. 126 (1987) 335–388. Google Scholar | DOI

[3] 3.Johnson, D., An abelian quotient of the mapping class group I, Math. Ann. 249 (1980) 225–242. Google Scholar | DOI

[4] 4.Johnson, D., The structure of the Torelli Group II. Topology 24 (1985) 113–126. Google Scholar | DOI

[5] 5.Johnson, D., The structure of the Torelli Group I. Ann. Math. 118 (1983) 423–442. Google Scholar | DOI

[6] 6.Lickorish, W. B. R., A finite set of generators for the homeotopy group of a 2-manifold, Proc. Camb. Phil. Soc.1 60 (1964) 769–778. Google Scholar | DOI

[7] 7.Magnus, W., Karrass, A. and Solitar, D., Combinatorial group theory, (Dover, 1976). Google Scholar

[8] 8.Mennicke, J., Zur Theorie der Siegelschen Modulgruppe, Math. Ann. 157 (1965) 115–129. Google Scholar | DOI

[9] 9.Newman, M., Integral matrices, (Academic Press, 1972). Google Scholar

[10] 10.Powell, J., Two theorems on the mapping class group of surfaces, Proc. AMS 68 (1978) 347–350. Google Scholar | DOI

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