Homeomorphisms of a surface which act trivially on homology
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- by Dennis L. Johnson PDF
- Proc. Amer. Math. Soc. 75 (1979), 119-125 Request permission
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
- Joan S. 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 482765, DOI 10.1090/S0002-9947-1978-0482765-9 W. Magnus, A. Karass and D. Solitar, Combinatorial group theory, Interscience, New York, 1966.
- Jerome Powell, Two theorems on the mapping class group of a surface, Proc. Amer. Math. Soc. 68 (1978), no. 3, 347–350. MR 494115, DOI 10.1090/S0002-9939-1978-0494115-8
Additional Information
- © Copyright 1979 American Mathematical Society
- 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