Two theorems on the mapping class group of a surface
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- by Jerome Powell PDF
- Proc. Amer. Math. Soc. 68 (1978), 347-350 Request permission
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
- Joan S. Birman, Abelian quotients of the mapping class group of a $2$-manifold, Bull. Amer. Math. Soc. 76 (1970), 147–150. MR 249603, DOI 10.1090/S0002-9904-1970-12406-5
- Joan S. Birman, Braids, links, and mapping class groups, Annals of Mathematics Studies, No. 82, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1974. MR 0375281
- Joan S. Birman, On Siegel’s modular group, Math. Ann. 191 (1971), 59–68. MR 280606, DOI 10.1007/BF01433472
- 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 171269, DOI 10.1017/s030500410003824x
Additional Information
- © Copyright 1978 American Mathematical Society
- 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