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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A “Tits-alternative” for subgroups of surface mapping class groups
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by John McCarthy PDF
Trans. Amer. Math. Soc. 291 (1985), 583-612 Request permission

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
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 291 (1985), 583-612
  • MSC: Primary 57M99; Secondary 20F38, 57N05
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0800253-8
  • MathSciNet review: 800253