Full box spaces of free groups
AbstractIn this paper we investigate full box spaces and coarse equivalences between them. We do this in two parts. In part one we compare the full box spaces of free groups on different numbers of generators. In particular, the full box space of a free group{F_{k}}is not coarsely equivalent to the full box space of a free group{F_{d}}, if{d\geq 8k+10}. In part two we compare{\Box_{f}\mathbb{Z}^{n}}to the full box spaces of 2-generated groups. In particular, we prove that the full box space of{\mathbb{Z}^{n}}is not coarsely equivalent to the full box space of any 2-generated group, if{n\geq 3}.
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