论文标题
免费产品的CTS
CTs for free products
论文作者
论文摘要
具有琐碎边缘组的有限组的有限组的基本组是免费产品。我们对这种自由产品的外部自动形态感兴趣，该产品将顶点组的共轭类别置于。我们表明，在特定感兴趣的情况下，例如顶点组本身是有限和环状群体的有限的免费产品，鉴于这种外部自动形态，在传递了正能力后，外部自动形态是由一个特别好的相对火车轨道图表示，称为A CT。 CTS首先是由Feighn和Handel引入的，用于自由组的外部自动形态。我们发展了吸引免费产品的层压和主要自动形态层压的理论。我们证明，自由产品的外部自动形态满足了指数不平等，让人联想到Gaboriau，Jaeger，Levitt和Lustig的结果，并增强了Martino的结果。最后，我们证明了一个结果让人联想到Culler的定理在自由产品的固定亚组上，其外部类具有有限顺序。
The fundamental group of a finite graph of groups with trivial edge groups is a free product. We are interested in those outer automorphisms of such a free product that permute the conjugacy classes of the vertex groups. We show that in particular cases of interest, such as where vertex groups are themselves finite free products of finite and cyclic groups, given such an outer automorphism, after passing to a positive power, the outer automorphism is represented by a particularly nice kind of relative train track map called a CT. CTs were first introduced by Feighn and Handel for outer automorphisms of free groups. We develop the theory of attracting laminations for and principal automorphisms of free products. We prove that outer automorphisms of free products satisfy an index inequality reminiscent of a result of Gaboriau, Jaeger, Levitt and Lustig and sharpening a result of Martino. Finally, we prove a result reminiscent of a theorem of Culler on the fixed subgroup of an automorphism of a free product whose outer class has finite order.
