On the isoperimetry of graphs with many ends
Tom 78 / 1998
Colloquium Mathematicum 78 (1998), 307-318
DOI: 10.4064/cm-78-2-307-318
Streszczenie
Let X be a connected graph with uniformly bounded degree. We show that if there is a radius r such that, by removing from X any ball of radius r, we get at least three unbounded connected components, then X satisfies a strong isoperimetric inequality. In particular, the non-reduced $l^2$-cohomology of X coincides with the reduced $l^2$-cohomology of X and is of uncountable dimension. (Those facts are well known when X is the Cayley graph of a finitely generated group with infinitely many ends.)
