论文标题
Lipschitz度量等法几乎是自由组的外部空间
Lipschitz metric isometries between Outer Spaces of virtually free groups
论文作者
论文摘要
道德（Dowdall）和泰勒（Taylor）观察到，鉴于一个自由组的有限索引亚组，覆盖范围会导致从自由组的外太空到亚组的外层空间的嵌入，因此，这种嵌入是相对于（非对称）Lipschitz度量的静脉测量，并且该嵌入式嵌入了该嵌入的轴线，该嵌入将折叠路径发送到折叠路径上。本注的目的是将此结果扩展到几乎免费的组。我们进一步扩展了Francaviglia和Martino的结果，证明了“候选人”的存在，用于Lipschitz在几乎自由群体的外层空间之间的点之间的距离。此外，我们还确定了Krstić和Vogtmann考虑的空间的虚拟群体外太空脊柱的变形缩回。
Dowdall and Taylor observed that given a finite-index subgroup of a free group, taking covers induces an embedding from the Outer Space of the free group to the Outer Space of the subgroup, that this embedding is an isometry with respect to the (asymmetric) Lipschitz metric, and that the embedding sends folding paths to folding paths. The purpose of this note is to extend this result to virtually free groups. We further extend a result Francaviglia and Martino, proving the existence of "candidates" for the Lipschitz distance between points in the Outer Space of the virtually free group. Additionally we identify a deformation retraction of the spine of the Outer Space for the virtually free group with the space considered by Krstić and Vogtmann.
