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<p>Infinite families of 3–dimensional closed graph manifolds and closed Seifert fibered spaces are exhibited, each member of which contains an essential torus not detected by ideal points of the variety of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10711_2025_1015_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\,\textrm{SL}\,}}_2(\mathbb {F})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mrow> <mspace width="0.166667em" /> <mtext>SL</mtext> <mspace width="0.166667em" /> </mrow> <mn>2</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">F</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>–characters over any algebraically closed field <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10711_2025_1015_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {F}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">F</mi> </math></EquationSource> </InlineEquation>.</p>

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Essential tori in 3–manifolds not detected in any characteristic

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月18日

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  • Grace S. Garden,
  • Benjamin Martin,
  • Stephan Tillmann

摘要

Infinite families of 3–dimensional closed graph manifolds and closed Seifert fibered spaces are exhibited, each member of which contains an essential torus not detected by ideal points of the variety of \({{\,\textrm{SL}\,}}_2(\mathbb {F})\) SL 2 ( F ) –characters over any algebraically closed field \(\mathbb {F}\) F .