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arXiv · 1208.4237

Spaces of Graphs, Boundary Groupoids and the Coarse Baum-Connes Conjecture

Martin Finn-Sell·Nick Wright
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Abstract

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.

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BibTeXRIS

Martin Finn-Sell, Nick Wright. 2013-07-08. Spaces of Graphs, Boundary Groupoids and the Coarse Baum-Connes Conjecture. https://doi.org/10.1016/j.aim.2014.02.029

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