A “Tits-alternative” for subgroups of surface mapping class groups
A “Tits-alternative” for subgroups of surface mapping class groups
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表面映射类组子组的“Tits-alternative”
DOI：
10.1090/s0002-9947-1985-0800253-8
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发表时间：
1985
影响因子：
1.3
通讯作者：
John E. McCarthy
中科院分区：
文献类型：
--
作者：
John E. McCarthy
。据观察，表面映射类群与线性群类（例如，[BLM，H]）共享各种共同的属性。在本文中，此类属性的已知列表被扩展到“Tits-Alternative”，这是由 J. Tits [T] 建立的线性群的属性。事实上，我们确定表面映射类群的每个子群要么实际上是阿贝尔群，要么包含非阿贝尔自由群。此外，为了建立这一结果，我们针对瑟斯顿射影叠层空间上的表面映射类的作用开发了一种吸引子和排斥子理论[Thl]。该理论概括了伪阿诺索夫映射的已知结果
. It has been observed that surface mapping class groups share various properties in common with the class of linear groups (e.g., [BLM, 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 [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 a.ction of surface mapping classes on Thurston's projective lamination spaces [Thl]. This theory generalizes results known for pseudo-Anosov mapping