Reflection rigidity of 2‐spherical Coxeter groups
Reflection rigidity of 2‐spherical Coxeter groups
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DOI：
10.1112/plms/pdl015
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发表时间：
2007-03
影响因子：
1.8
通讯作者：
P. Caprace;B. Mühlherr
中科院分区：
文献类型：
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作者：
P. Caprace;B. Mühlherr
证明了当群W为无限阶群时，每一个n-生成的不可约的2-球面Coxeter系统（W，S）都是强反射刚性的.这特别意味着这样一个群的所有保持反射的自同构都是内由图。我们的结果可以被看作是第一个主要步骤证明的猜想，所有的无限，不可约Coxeter系统是强反射刚性，如果他们不承认图扭曲。
We prove that each finitely generated, irreducible and 2‐spherical Coxeter system (W, S) is strongly reflection rigid whenever the group W is of infinite order. This means in particular that all reflection‐preserving automorphisms of such a group are inner‐by‐graph. Our result can be seen as a first major step towards a proof of the conjecture that all infinite, irreducible Coxeter systems are strongly reflection rigid if they do not admit diagram twists.