On the isoperimetry of graphs with many ends

Volume 78 / 1998

Christophe Pittet Colloquium Mathematicum 78 (1998), 307-318 DOI: 10.4064/cm-78-2-307-318


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.)


  • Christophe Pittet

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