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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0529227-4
PII: S 0002-9939(1979)0529227-4
Article copyright: © Copyright 1979 American Mathematical Society