论文标题
较高等级晶格的行动全球刚度与主导分裂
Global rigidity of actions by higher rank lattices with dominated splitting
论文作者
论文摘要
我们证明，在封闭的$ n $ manifold上，具有一个承认主导拆分的元素的元素，在$ \ mathbb {r}）$，$ n \ ge 3 $中的任何平滑体积保留动作（$ \ textrm {sl}（n，\ mathbb {r}）$，$ n \ ge 3 $，应该是标准的。换句话说，歧管是$ n $ -flat的圆环，该动作与仿射动作相结合。请注意，Anosov的差异性或更普遍的是部分双曲线差异性，可以主导分裂。当$α$为$ c^{1} $时，我们的拓扑全球刚度。类似的定理可以使用$ \ textrm {sp}（2n，\ mathbb {r}）$与$ n \ ge 2 $和$ \ textrm {so}（so}（n，n）$一起使用$ n \ ge 5 $ in Chole $ 2n $ -manifold。
We prove that any smooth volume-preserving action of a lattice $Γ$ in $\textrm{SL}(n,\mathbb{R})$, $n\ge 3$, on a closed $n$-manifold which possesses one element that admits a dominated splitting should be standard. In other words, the manifold is the $n$-flat torus and the action is smoothly conjugate to an affine action. Note that an Anosov diffeomorphism, or more generally, a partial hyperbolic diffeomorphism admits a dominated splitting. We have a topological global rigidity when $α$ is $C^{1}$. Similar theorems hold for an action of a lattice in $\textrm{Sp}(2n,\mathbb{R})$ with $n\ge 2$ and $\textrm{SO}(n,n)$ with $n\ge 5$ on a closed $2n$-manifold.
