Bounding the complexity of simplicial group actions on trees
Bounding the complexity of simplicial group actions on trees
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限制树上简单群动作的复杂性
DOI：
10.1007/bf01239522
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发表时间：
1991
影响因子：
3.1
通讯作者：
Mark Feighn
中科院分区：
文献类型：
--
作者：
M. Bestvina;Mark Feighn
我们将陈述本文的主要结果在单纯树上的群作用。假设群G单纯作用在树T上，没有逆。为了简洁起见，我们说T是一个G-树。则轨道空间T/G是一个图，其顶点和边对应于T中的顶点和边的G-等价类。T/G中的每一个顶点和边都用相应等价类的代表的稳定子来标记。这个标号是G的一个子群，只在G中共轭时才被定义（详见[7]或[8]）。因此T/G是基本群为G的群的图。我们有兴趣找到一个号码吗？(G)，仅依赖于G，使得对于每一个G-树T，图T/G不超过？(G)顶点和边。有些意见是适当的。
We shall state the main result of this paper in terms of group actions on simplicial trees. Suppose that a group G acts simplicially on a tree T without inversions. For brevity we say that Tis a G-tree. Then the orbit space T/G is a graph whose vertices and edges correspond to G-equivalence classes of vertices and edges in T. Each vertex and edge in T/G is labeled by the stabilizer of a representative of the corresponding equivalence class. This label, a subgroup of G, is well-defined only up to conjugation in G (for details, see [7] or [8]). Thus T/G is a graph of groups whose fundamental group is G. We are interested in finding a number ?(G), depending only on G, so that for every G-tree T, the graph T/G has no more than ?(G) vertices and edges. Some remarks are in order.