辫图群与局部相似群
Braided Diagram Groups and Local Similarity Groups
摘要：
Hughes定义了一类在紧致超度量空间上充当局部相似性的群。Guba和Sapir以前定义了半群表示上的辫图群。这两类群有一些共同的特征：它们在CAT（0）三次复形上都是等距的，并且两类中的某些群都有F-无穷型。在这里，我们澄清了这些群族之间的关系：树状半群表示上的辫子图群正是通过小相似结构作用于紧致超度量空间的群。该证明可以被认为是证明汤普森群V是树状半群表示上的辫子图群的推广。我们还证明了某些额外的群体，如霍顿群，和一定的一组准自同构位于这两个类。
英文摘要：
Hughes defined a class of groups that act as local similarities on compact ultrametric spaces. Guba and Sapir had previously defined braided diagram groups over semigroup presentations. The two classes of groups share some common characteristics: both act properly by isometries on CAT(0) cubical complexes, and certain groups in both classes have type F-infinity, for instance. Here we clarify the relationship between these families of groups: the braided diagram groups over tree-like semigroup presentations are precisely the groups that act on compact ultrametric spaces via small similarity structures. The proof can be considered a generalization of the proof that Thompson's group V is a braided diagram group over a tree-like semigroup presentation. We also prove that certain additional groups, such as the Houghton groups, and a certain group of quasi-automorphisms lie in both classes.
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