二面体型Artin群的Busemann点
Busemann points of Artin groups of dihedral type
摘要：
研究了二面体型Artin群的时函数边界，其字度量来自于通常的Artin生成元或对偶生成元。在这两种情况下，我们确定horobouncement，并说哪些点是Busemann点，这是测地线的极限。在对偶生成元的情况下，所有的边界点都是Busemann点，但这对Artin生成元不是真的。我们还将测地线的对偶生成元，这使我们能够计算相关的测地线增长系列。
英文摘要：
We study the horofunction boundary of an Artin group of dihedral type with its word metric coming from either the usual Artin generators or the dual generators. In both cases, we determine the horoboundary and say which points are Busemann points, that is the limits of geodesic rays. In the case of the dual generators, it turns out that all boundary points are Busemann points, but this is not true for the Artin generators. We also characterise the geodesics with respect to the dual generators, which allows us to calculate the associated geodesic growth series.
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