论文标题
通过更高的条形变形构建适当的仿射动作
Constructing proper affine actions via higher strip deformations
论文作者
论文摘要
我们引入了较高的带状变形，这给出了一种在不可减至的表示形象中构建离散自由组的仿射变形的方法。我们使用Margulis不变式来找到这些变形的适当条件，表明每个凸CoCoCompact Free Group允许在$ \ Mathbb {r}^{4n-1} $上正确作用的仿射变形。使用我们的方法，我们还可以构建几乎免费组的适当仿射动作，我们通过在$ \ m athbb上找到$ C_2 \ star c_3 $的适当动作来证明这一点。
We introduce higher strip deformations, which give a way of constructing affine deformations of discrete free groups in the image of the irreducible representation $\operatorname{PSL}_2\mathbb{R}\to \operatorname{SO}(2n,2n-1)$. We use the Margulis invariant to find a properness condition for these deformations, showing that each convex cocompact free group admits affine deformations acting properly on $\mathbb{R}^{4n-1}$. Using our method we can also construct proper affine actions of virtually free groups, which we demonstrate by finding proper actions of $C_2 \star C_3$ on $\mathbb{R}^7.$
