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Two theorems on the mapping class group of a surface


Author: Jerome Powell
Journal: Proc. Amer. Math. Soc. 68 (1978), 347-350
MSC: Primary 57A05; Secondary 30A46
DOI: https://doi.org/10.1090/S0002-9939-1978-0494115-8
MathSciNet review: 0494115
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Abstract: The mapping class group of a closed surface of genus $ \geqslant 3$ is perfect. An infinite set of generators is given for the subgroup of maps that induce the identity on homology.


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

  • [1] J. Birman, Abelian quotients of the mapping class group of a 2 manifold, Bull. Amer. Math. Soc. 76 (1970), 147-150; Erratum 77 (1971), 479. MR 0249603 (40:2846)
  • [2] -, Braids, links and mapping class groups, Ann. of Math. Studies, No. 82, Princeton Univ. Press, Princeton, N. J., 1974. MR 0375281 (51:11477)
  • [3] -, On Siegel's Modular Group, Math. Ann. 191 (1971), 59-68. MR 0280606 (43:6325)
  • [4] W. B. R. Lickorish, A finite set of generators for the homeotopy group of a 2-manifold, Proc. Cambridge Philos. Soc. 60 (1964), 769-778. MR 0171269 (30:1500)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0494115-8
Keywords: Mapping class group, identity on homology, Dehn twists
Article copyright: © Copyright 1978 American Mathematical Society

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