Deformation spaces of discrete groups and hyperbolic structures

首席研究员藤井获得了几个与阿廷集团有关的结果。首先，对于每个Artin幺半群，Fujii具体地构造了它的测地线自动结构，并得到了它的增长函数的有理函数表达式。其次，Fujii考虑了Artin群的每个元素在其标准生成系统中的代表，并给出了一个必要条件，使得代表相对于生成系统是最短的。

The head investigator Fujii obtained several results that concerns Artin groups. First, for each Artin monoid, Fujii concretely constructed its geodesic automatic structure and obtained a rational function expression of its growth function. Next, Fujii considers representatives of each elements of Artin groups in terms of its standard generator system and gave a necessary condition such that representatives are shortest with respect to the generator system.