Full box spaces of free groups

What is it about?

In 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 on k generators is not coarsely equivalent to the full box space of a free group on d generators, if d > 8k + 10. In part two we compare the full box space of the free abelian group of rank n to the full box spaces of 2-generated groups and prove that they can not be coarsely equivalent if n>2.

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