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Normal closures of powers of Dehn twists in mapping class groups

Published online by Cambridge University Press:  18 May 2009

Stephen P. Humphries
Stephen P. Humphries
Affiliation:
Department of Mathematics, Brigham Young University, Provo, Utah, 84602, U.S.A.
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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).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 3 , September 1992 , pp. 314 - 317
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

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