论文标题
双曲线一轮组
Hyperbolic one-relator groups
论文作者
论文摘要
我们介绍了两个分别的单层仪组的家族，称为原始扩展组，并表明，如果其原始扩展亚组是双曲线，则单余组是双曲线。这减少了表征双曲线单层子组以表征双曲线原始扩展组的问题。此外，这些新组将明确的分解作为具有相邻根的自由组的图形。为了获得此结果，我们表征了$ 2 $ Free的单式式群体，该组在Christoffel单词方面具有非凡的交集，表明双曲线单式式群体具有准convex Magnus子组，并建立在作者先前文章中的单式塔楼机械上。
We introduce two families of two-generator one-relator groups called primitive extension groups and show that a one-relator group is hyperbolic if its primitive extension subgroups are hyperbolic. This reduces the problem of characterising hyperbolic one-relator groups to characterising hyperbolic primitive extension groups. These new groups moreover admit explicit decompositions as graphs of free groups with adjoined roots. In order to obtain this result, we characterise $2$-free one-relator groups with exceptional intersection in terms of Christoffel words, show that hyperbolic one-relator groups have quasi-convex Magnus subgroups and build upon the one-relator tower machinery developed in the authors previous article.
