Spaces of graphs, boundary groupoids and the coarse Baum-Connes conjecture

作者：Finn Sell Martin^*; Wright Nick

来源：Advances in Mathematics, 2014, 259: 306-338.

DOI：10.1016/j.aim.2014.02.029

• Noncommutative geometry
• Roe algebras
• Large girth expanders
• Partial actions of discrete groups

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 Cosines 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.

• 出版日期2014-7-10