论文标题
$ sl（n，{\ bf r}）$和$ sl（n，{\ bf z}）$的平滑和分析动作
Smooth and analytic actions of $SL(n,{\bf R})$ and $SL(n,{\bf Z})$ on closed $n$-dimensional manifolds
论文作者
论文摘要
主要结果是将$ sl（n，{\ bf r}）$，$ n \ geq 3 $的平滑操作分类，或在封闭的$ n $ -manifolds上本地同构的相关组，扩展了Uchida定理。我们在$ n $ -torus上构建了$ sl（n，{\ bf z}）$的新外来动作，并在$ n $ -tori的$ n $ tori和连接的总和上进行连接的总和，我们在$ n $ n $ -manifolds上对lattices oction to the $ n $ -tori进行了猜想。我们证明了有关$ sl（n，{\ bf r}）$ - 动作的不变刚性几何结构的一些结果。
The main result is a classification of smooth actions of $SL(n,{\bf R})$, $n \geq 3$, or connected groups locally isomorphic to it, on closed $n$-manifolds, extending a theorem of Uchida. We construct new exotic actions of $SL(n,{\bf Z})$ on the $n$-torus and connected sums of $n$-tori, and we formulate a conjectural classification of actions of lattices in $SL(n,{\bf R})$ on closed $n$-manifolds. We prove some results about invariant rigid geometric structures for $SL(n,{\bf R})$-actions.
