On a coarse invertibility spectrum for coarse groups

Abstract

We introduce a coarse algebraic invariant for coarse groups and use it to differentiate various coarsifications of the group of integers. This lets us answer two questions posed by Leitner and the second author. The invariant is obtained by considering the set of exponents n such that taking n-th powers defines a coarse equivalence of the coarse group.

15 pages, fixed a small mistake in the proof of Lemma 3.5