Orbit counting in conjugacy classes for free groups acting on trees
Orbit counting in conjugacy classes for free groups acting on trees
复制标题
作用于树的自由群的共轭类中的轨道计数
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Richard Sharp
中科院分区：
文献类型：
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作者：
George Kenison;Richard Sharp
本文研究了有限度量图的基本群在其泛覆盖树上的作用。我们假设图是有限的，连通的，并且每个顶点的度至少为3。此外，我们还假定了边长的无理性条件。当泛覆盖树中给定基顶点的相关位移至多为$T$时，我们得到了固定共轭类中元素个数的一个渐近估计。在一个温和的额外假设下，我们还得到了一个多项式误差项。
In this paper we study the action of the fundamental group of a finite metric graph on its universal covering tree. We assume the graph is finite, connected and the degree of each vertex is at least three. Further, we assume an irrationality condition on the edge lengths. We obtain an asymptotic for the number of elements in a fixed conjugacy class for which the associated displacement of a given base vertex in the universal covering tree is at most $T$. Under a mild extra assumption we also obtain a polynomial error term.