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<p>We demonstrate the existence of minimal simplicial <i>n</i>-complexes which inevitably contain a non-splittable two-component link formed by an <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\((n-1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-sphere and an <i>n</i>-sphere in any embedding into <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathbb {R}^{2n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </msup> </math></EquationSource> </InlineEquation>. This provides a higher-dimensional generalization of graphs that are not non-separating planar.</p>

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Intrinsic linking of a simplicial n-complex embedded in \(\mathbb {R}^{2n}\)

  • 期刊论文

  • 发表日期：

    2026年8月5日

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  • Ryo Nikkuni

摘要

We demonstrate the existence of minimal simplicial n-complexes which inevitably contain a non-splittable two-component link formed by an \((n-1)\) ( n - 1 ) -sphere and an n-sphere in any embedding into \(\mathbb {R}^{2n}\) R 2 n . This provides a higher-dimensional generalization of graphs that are not non-separating planar.