论文标题
与Anosov自律组II的完整仿射歧管II：部分双曲线颗粒和共同体学维度
Complete affine manifolds with Anosov holonomy groups II: partially hyperbolic holonomy and cohomological dimensions
论文作者
论文摘要
让$ n $为一个完整的仿射歧管$ a^n/γ$ dimension $ n $，其中$γ$是一个仿射转换组，$ k（γ，1）$被实现为有限的CW-Complex。 $ n $具有部分双曲线固体组，如果切线束在单位切线束上方，将足够大的紧凑型零件拆分为沿着测量流量的扩展，中性和收缩的子捆绑式。我们表明，如果整体组是索引$ k $的部分双曲线，则$ k <n/2 $，则是$ \ mathrm {cd}（γ）\ leq n-k $。此外，如果有限的仿射组$γ$与$ k $ -Anosov线性组适当地，$ k \ leq n/2 $适当地自由，然后$ K $ -Anosov Linear Group，然后$ \ Mathrm {cd}（γ）（γ）\ leq n-k $。此外，还存在$ n-k $二维仿射子空间的紧凑型集合，其中$γ$可以使用。这里的技术主要来自粗糙的几何形状。
Let $N$ be a complete affine manifold $A^n/Γ$ of dimension $n$ where $Γ$ is an affine transformation group and $K(Γ, 1)$ is realized as a finite CW-complex. $N$ has a partially hyperbolic holonomy group if the tangent bundle pulled over the unit tangent bundle over a sufficiently large compact part splits into expanding, neutral, and contracting subbundles along the geodesic flow. We show that if the holonomy group is partially hyperbolic of index $k$, $k < n/2$, then $\mathrm{cd}(Γ) \leq n-k$. Moreover, if a finitely-presented affine group $Γ$ acts on $A^n$ properly discontinuously and freely with the $k$-Anosov linear group for $k \leq n/2$, then $\mathrm{cd}(Γ) \leq n-k$. Also, there exists a compact collection of $n-k$-dimensional affine subspaces where $Γ$ acts on. The techniques here are mostly from coarse geometry.
