论文标题
在$ {\ rm sl}的Borel Anosov子组上（D，\ Mathbb {r}）$
On Borel Anosov subgroups of ${\rm SL}(d,\mathbb{R})$
论文作者
论文摘要
我们研究了完整标志歧管的抗podal子集$ \ mathcal {f}（\ mathbb {r}^d）$。结果，对于自然数量$ d \ ge 2 $，以至于$ d \ ne 5 $和$ d \ equiv 0，\ pm1 \ mod 8 $，我们表明$ {\ rm sl}（\ rm sl}（d，d，d，d，\ m athbb {r}）$的borel anosov子组实际上是一个免费的组，或者是一个免费的组。这给了安德烈斯·萨姆巴里诺（AndrésSambarino）问的一个问题。此外，我们显示了对双曲线空间的限制，将均匀的常规准静电嵌入到对称空间中$ x_d $ of $ {\ rm sl}（d，d，\ mathbb {r}）$。
We study the antipodal subsets of the full flag manifolds $\mathcal{F}(\mathbb{R}^d)$. As a consequence, for natural numbers $d \ge 2$ such that $d\ne 5$ and $d \not\equiv 0,\pm1 \mod 8$, we show that Borel Anosov subgroups of ${\rm SL}(d,\mathbb{R})$ are virtually isomorphic to either a free group or the fundamental group of a closed hyperbolic surface. This gives a partial answer to a question asked by Andrés Sambarino. Furthermore, we show restrictions on the hyperbolic spaces admitting uniformly regular quasi-isometric embeddings into the symmetric space $X_d$ of ${\rm SL}(d,\mathbb{R})$.
