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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


A ``Tits-alternative'' for subgroups of surface mapping class groups

Author: John McCarthy
Journal: Trans. Amer. Math. Soc. 291 (1985), 583-612
MSC: Primary 57M99; Secondary 20F38, 57N05
MathSciNet review: 800253
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Abstract: It has been observed that surface mapping class groups share various properties in common with the class of linear groups (e.g., $ [\mathbf{BLM},\,\mathbf{H}]$). In this paper, the known list of such properties is extended to the ``Tits-Alternative'', a property of linear groups established by J. Tits $ [\mathbf{T}]$. In fact, we establish that every subgroup of a surface mapping class group is either virtually abelian or contains a nonabelian free group.

In addition, in order to establish this result, we develop a theory of attractors and repellers for the action of surface mapping classes on Thurston's projective lamination spaces $ [\mathbf{Th1}]$. This theory generalizes results known for pseudo-Anosov mapping classes $ [\mathbf{FLP}]$.

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Additional Information

PII: S 0002-9947(1985)0800253-8
Keywords: Surface mapping class group, geodesic lamination, virtually abelian
Article copyright: © Copyright 1985 American Mathematical Society

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