关于CAT $(κ)$空间和欧氏建筑的局部结构和同调
On the local structure and the homology of CAT$(κ)$ spaces and euclidean buildings
摘要：
证明了欧氏建筑物的每个开子集都是有限维绝对邻域收缩核。这特别意味着这样的集合具有有限维单纯复形的同伦类型。我们还包括一个证明的刚性同胚的欧几里德建筑。在我们的方法，这个结果的一个关键步骤是：一个CAT $(κ)$空间$X$的方向$Σ_oX$同伦等价于一个小穿孔磁盘$B_\eps(X,o)\setminus o$。第二个成分是$X$的局部同调层。在此过程中，我们证明了CAT $(κ)$ -空间的局部结构的一些结果，这可能是独立的利益。
英文摘要：
We prove that every open subset of a euclidean building is a finite dimensional absolute neighborhood retract. This implies in particular that such a set has the homotopy type of a finite dimensional simplicial complex. We also include a proof for the rigidity of homeomorphisms of euclidean buildings. A key step in our approach to this result is the following: the space of directions $Σ_oX$ of a CAT$(κ)$ space $X$ is homotopy quivalent to a small punctured disk $B_\eps(X,o)\setminus o$. The second ingredient is the local homology sheaf of $X$. Along the way, we prove some results about the local structure of CAT$(κ)$-spaces which may be of independent interest.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
