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<p>We develop a framework for common commensurators of discrete subgroups of lattices in isometry groups of CAT(0) spaces. We show that the Greenberg–Shalom hypothesis about discreteness of common commensurators of Zariski dense subgroups and lattices fails in this generality, even if one imposes strong finiteness conditions. We analyze some examples due to Burger and Mozes in this context and show that they have discrete common commensurator.</p>

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Indiscrete Common Commensurators

  • 期刊论文

  • 发表日期：

    2026年6月21日

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  • Jingyin Huang,
  • Mahan Mj

摘要

We develop a framework for common commensurators of discrete subgroups of lattices in isometry groups of CAT(0) spaces. We show that the Greenberg–Shalom hypothesis about discreteness of common commensurators of Zariski dense subgroups and lattices fails in this generality, even if one imposes strong finiteness conditions. We analyze some examples due to Burger and Mozes in this context and show that they have discrete common commensurator.