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<p>Let <i>K′</i> be a satellite knot of a knot <i>K</i>. If <i>K</i> is a high distance knot, then the tunnel numbers <i>t</i>(<i>K′</i>) and <i>t</i>(<i>K</i>) satisfy <i>t</i>(<i>K′</i>) ≥ <i>t</i>(<i>K</i>) + 1. The authors also give an example showing that the inequality above is sharp.</p>

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Strict Inequality Between Tunnel Numbers of a Satellite Knot and Its High Distance Companion

  • 期刊论文

  • 发表日期：

    2026年7月13日

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  • Chunxing Yan,
  • Wenjie Diao,
  • Yanqing Zou

摘要

Let K′ be a satellite knot of a knot K. If K is a high distance knot, then the tunnel numbers t(K′) and t(K) satisfy t(K′) ≥ t(K) + 1. The authors also give an example showing that the inequality above is sharp.