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<p>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 <i>n</i> such that taking <i>n</i>-th powers defines a coarse equivalence of the coarse group.</p>

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On a coarse invertibility spectrum for coarse groups

  • 期刊论文

  • 发表日期：

    2025年5月16日

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  • Leo Schäfer,
  • Federico Vigolo

摘要

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.