Spaces of Graphs, Boundary Groupoids and the Coarse Baum-Connes Conjecture
Spaces of Graphs, Boundary Groupoids and the Coarse Baum-Connes Conjecture
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DOI：
10.1016/j.aim.2014.02.029
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发表时间：
2012-08
影响因子：
1.7
通讯作者：
Martin Finn-Sell;N. Wright
中科院分区：
文献类型：
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作者：
Martin Finn-Sell;N. Wright
我们引入了粗鲍姆-康尼斯猜想的一个新变体，旨在解决粗略断开的度量空间，称为边界粗鲍姆-康尼斯猜想。我们针对许多粗略不连续的空间证明了这个猜想，这些空间已知是粗略鲍姆-康尼斯猜想的反例。特别地，我们针对具有大周长和有界顶点度的图空间给出了该猜想的几何证明。然后，我们使用同调方法将边界猜想与粗鲍姆-康内斯猜想联系起来，这使我们能够以基本的方式展示当前所有一致离散的粗鲍姆-康内斯猜想的反例。
We introduce a new variant of the coarse Baum–Connes conjecture designed to tackle coarsely disconnected metric spaces called the boundary coarse Baum–Connes conjecture. We prove this conjecture for many coarsely disconnected spaces that are known to be counterexamples to the coarse Baum–Connes conjecture. In particular, we give a geometric proof of this conjecture for spaces of graphs that have large girth and bounded vertex degree. We then connect the boundary conjecture to the coarse Baum–Connes conjecture using homological methods, which allows us to exhibit all the current uniformly discrete counterexamples to the coarse Baum–Connes conjecture in an elementary way.