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Proceedings of the American Mathematical Society

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Homeomorphisms of a surface which act trivially on homology


Author: Dennis L. Johnson
Journal: Proc. Amer. Math. Soc. 75 (1979), 119-125
MSC: Primary 57N05
DOI: https://doi.org/10.1090/S0002-9939-1979-0529227-4
MathSciNet review: 529227
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Abstract: Let $ \mathfrak{M}$ be the mapping class group of a surface of genus $ g \geqslant 3$, and $ \mathcal{I}$ the subgroup of those classes acting trivially on homology. An infinite set of generators for $ \mathcal{I}$, involving three conjugacy classes, was obtained by Powell. In this paper we improve Powell's result to show that $ \mathcal{I}$ is generated by a single conjugacy class and that $ [\mathfrak{M},\mathcal{I}] = \mathcal{I}$.


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

  • [BC] J. Birman and R. Craggs, The $ \mu $-invariant of 3-manifolds and certain structural properties of the group of homeomorphisms of a closed, oriented 2-manifold, Trans. Amer. Math. Soc. 237 (1978), 283-309. MR 0482765 (58:2818)
  • [MKS] W. Magnus, A. Karass and D. Solitar, Combinatorial group theory, Interscience, New York, 1966.
  • [P] J. Powell, Two theorems on the mapping class group of surfaces, Proc. Amer. Math. Soc. 68 (1978), 347-350. MR 0494115 (58:13045)

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DOI: https://doi.org/10.1090/S0002-9939-1979-0529227-4
Article copyright: © Copyright 1979 American Mathematical Society

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