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自由群中的线型

Line Patterns in Free Groups

Christopher H. Cashen, Natasa Macura

备注：
35 pages, 22 figures, PDFLatex; v2. finite index requires extra hypothesis; v3. 37 pages, 24 figures: updated references and add example in Section 6.3 of a rigid pattern for which the free group is not finite index in the group of pattern preserving quasi-isometries; v4. 40 pages, 26 figures: improved exposition and add example in Section 6.4 of a rigid pattern whose cube complex is not a tree
发表信息：
Geom. Topol. 15 (2011) 1419-1475
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摘要：

我们研究了自由群中的线模式，通过考虑分解空间的拓扑，一个商的边界在无穷远的自由群有关的线模式。我们证明了在自由群中保持线模式的拟等距群在相关空间上作用等距当且仅当分解空间中没有割对。

英文摘要：

We study line patterns in a free group by considering the topology of the decomposition space, a quotient of the boundary at infinity of the free group related to the line pattern. We show that the group of quasi-isometries preserving a line pattern in a free group acts by isometries on a related space if and only if there are no cut pairs in the decomposition space.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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