Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}]$.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57M99, 20F38, 57N05

Retrieve articles in all journals with MSC: 57M99, 20F38, 57N05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0800253-8
PII: S 0002-9947(1985)0800253-8
Keywords: Surface mapping class group, geodesic lamination, virtually abelian
Article copyright: © Copyright 1985 American Mathematical Society