Limit groups as limits of free groups: compactifying the set of free groups.
Limit groups as limits of free groups: compactifying the set of free groups.
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限制群作为自由群的限制：压缩自由群的集合。
DOI：
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发表时间：
2004
期刊：
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通讯作者：
Vincent Guirardel
中科院分区：
文献类型：
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作者：
C. Champetier;Vincent Guirardel
本文给出了研究Sela极限群的一个拓扑框架：极限群是自由群在标记群的紧空间中的极限.许多结果在这种情况下得到了自然的解释.极限群的类与有限生成的完全剩余自由群的类是一致的.拓扑方法对完全剩余自由群、自由群的普遍理论、超积和非标准自由群之间的关系提供了一些新的见解.
We give a topological framework for the study of Sela's limit groups:limit groups are limits of free groups in a compact space of markedgroups.Many results get a natural interpretation in this setting.The class of limit groups is known to coincide with the class offinitely generated fully residually free groups.The topological approach gives some new insight on the relation betweenfully residually free groups, the universal theory of free groups,ultraproducts and non-standard free groups.