论文标题
树木，cantor套装和可解决的鲍姆斯拉格群体的嵌入
Embeddings of Trees, Cantor Sets and Solvable Baumslag-Solitar Groups
论文作者
论文摘要
我们表征了两个可溶解的鲍姆斯兰 - 统计组之间存在的准静态嵌入。这扩展了Farb和Mosher对同一组之间的准定图。更一般而言，我们表征何时可以存在两个树状空间之间的绝对计嵌入。这使我们能够确定何时两个绿色空间是准测量法，从而确认了疑虑的疑虑。事实证明，是否存在两个树状空间之间存在的准静态嵌入的问题相当于是否存在两个符号康托群之间的bilipschitz嵌入，这反过来又等同于是否存在两条粗糙的等距嵌入在两条常规生根树之间的问题。因此，我们同时回答所有这三个问题。事实证明，这种嵌入的存在完全取决于有趣的整数序列家族的界限。
We characterise when there exists a quasiisometric embedding between two solvable Baumslag-Solitar groups. This extends the work of Farb and Mosher on quasiisometries between the same groups. More generally, we characterise when there can exist a quasiisometric embedding between two treebolic spaces. This allows us to determine when two treebolic spaces are quasiisometric, confirming a conjecture of Woess. The question of whether there exists a quasiisometric embedding between two treebolic spaces turns out to be equivalent to the question of whether there exists a bilipschitz embedding between two symbolic Cantor sets, which in turn is equivalent to the question of whether there exists a rough isometric embedding between two regular rooted trees. Hence we answer all three of these questions simultaneously. It turns out that the existence of such embeddings is completely determined by the boundedness of an intriguing family of integer sequences.
