论文标题
粗捆的共同体
Coarse sheaf cohomology
论文作者
论文摘要
分配给度量空间的某种斜体拓扑导致了束缚的共同体学理论，该理论看到了该空间的粗糙结构。已经恒定的系数会产生有趣的同胞组。在0度中，他们看到了空间的末端数量。在本文中，开发了通过Cochains恒定捆的分辨率。它是计算共同体学的宝贵工具。另外，还建立了具有恒定系数的粗共同体的粗糙同质性不变性。该属性可用于计算里曼尼亚歧管的共同体。适当的度量空间的Higson Corona显示出可以反映滑轮和捆出的同谋。因此，我们可以在计算中使用紧凑的Hausdorff空间上使用拓扑工具。特别是，如果适当的度量空间的渐近维度是有限的，那么更高的同胞组就消失了。我们计算了一些例子。事实证明，有限的亚伯群最适合有限生成的组的系数。
A certain Grothendieck topology assigned to a metric space gives rise to a sheaf cohomology theory which sees the coarse structure of the space. Already constant coefficients produce interesting cohomology groups. In degree 0 they see the number of ends of the space. In this paper a resolution of the constant sheaf via cochains is developed. It serves to be a valuable tool for computing cohomology. In addition coarse homotopy invariance of coarse cohomology with constant coefficients is established. This property can be used to compute cohomology of Riemannian manifolds. The Higson corona of a proper metric space is shown to reflect sheaves and sheaf cohomology. Thus we can use topological tools on compact Hausdorff spaces in our computations. In particular if the asymptotic dimension of a proper metric space is finite then higher cohomology groups vanish. We compute a few examples. As it turns out finite abelian groups are best suited as coefficients on finitely generated groups.
