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An example about normalizers in mapping class groups

Author: Jane Gilman
Journal: Proc. Amer. Math. Soc. 69 (1978), 115-118
MSC: Primary 30A46; Secondary 57A05
MathSciNet review: 0486493
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Abstract: J. Birman has raised the question as to whether every element of the mapping class group (the Teichmüller modular group) is in the normalizer of some element of finite order. In this paper elements of the mapping class group which are not in the normalizer of any element of finite order are constructed.

References [Enhancements On Off] (What's this?)

  • [1] J. Birman, Braids, links, and mapping class groups, Ann. of Math. Studies, no. 82, Princeton Univ. Press, Princeton, N. J.,1974. MR 0375281 (51:11477)
  • [2] J. Gilman, A matrix representation for automorphisms of compact Riemann surfaces, Linear Algebra and Appl. 17 (1977), 139-147. MR 0499135 (58:17077)
  • [3] F. Raymond and J. L. Tollefson, Closed 3-manifolds with no periodic maps, Trans. Amer. Math. Soc. 221 (1976), 403-418. MR 0415620 (54:3703)

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Keywords: Mapping class groups, Teichmüller modular group, Riemann surface, automorphism
Article copyright: © Copyright 1978 American Mathematical Society

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