Scholarlink

<p>This paper proves a uniqueness result for 2-spheres that split a knotted handlebody in the 3-sphere along three parallel disks. We apply the result to study the symmetry of knotted handlebodies, measured by the mapping class group. In particular, the chirality of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10711_2025_1033_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbf {6_{10}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mn mathvariant="bold">6</mn> <mn mathvariant="bold">10</mn> </msub> </math></EquationSource> </InlineEquation> in the handlebody-knot table, which was previously unknown, is determined. An infinite family of hyperbolic handlebody-knots with homeomorphic exteriors is also constructed.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Unique 3-decomposition and mapping classes of knotted handlebodies

  • 期刊论文

  • 发表日期：

    2025年8月26日

查看全文
  • Giovanni Bellettini,
  • Maurizio Paolini,
  • Yi-Sheng Wang

摘要

This paper proves a uniqueness result for 2-spheres that split a knotted handlebody in the 3-sphere along three parallel disks. We apply the result to study the symmetry of knotted handlebodies, measured by the mapping class group. In particular, the chirality of \(\mathbf {6_{10}}\) 6 10 in the handlebody-knot table, which was previously unknown, is determined. An infinite family of hyperbolic handlebody-knots with homeomorphic exteriors is also constructed.