Euler Characteristics and imbeddings of hyperbolic Coxeter groups
Euler Characteristics and imbeddings of hyperbolic Coxeter groups
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双曲 Coxeter 群的欧拉特征和嵌入
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
G. Maxwell
中科院分区：
文献类型：
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作者：
G. Maxwell
摘要本文有两个目的。第一个是用理论和计算机辅助相结合的方法计算水平1或2的双曲Coxeter群Ws的Euler特征线。对于水平1和奇数值的组|S|在双曲空间中，欧拉特征线与Ws的基本区域的体积有关。其次，我们注意到两种方法嵌入这样的群体在对方。这减少了确定欧拉特征线所需的计算量，也减少了需要考虑的本质上不同的双曲群的数量。
Abstract This paper has a twofold purpose. The first is to compute the Euler characteristics of hyperbolic Coxeter groups Ws of level 1 or 2 by a mixture of theoretical and computer aided methods. For groups of level 1 and odd values of |S|, the Euler characteristic is related to the volume of the fundamental region of Ws in hyperbolic space. Secondly we note two methods of imbedding such groups in each other. This reduces the amount of computation needed to determine the Euler characteristics and also reduces the number of essentially different hyperbolic groups that need to be considered.