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<p>This article introduces new invariants for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\( k \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> </InlineEquation>-colored links. In particular, the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( k \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> </InlineEquation>-quandle counting invariants for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\( k \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> </InlineEquation>-colored links are constructed. Furthermore, the notion of topological <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\( k \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> </InlineEquation>-quandles is introduced and used to construct another coloring invariant, a topological space that can be interpreted as the space of colorings of the <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\( k \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> </InlineEquation>-colored link by the topological <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\( k \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>k</mi> </math></EquationSource> </InlineEquation>-quandle.</p>

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Colored link invariants

  • 期刊论文

  • 发表日期：

    2025年12月10日

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  • Georgy C Luke,
  • B. Subhash

摘要

This article introduces new invariants for \( k \) k -colored links. In particular, the \( k \) k -quandle counting invariants for \( k \) k -colored links are constructed. Furthermore, the notion of topological \( k \) k -quandles is introduced and used to construct another coloring invariant, a topological space that can be interpreted as the space of colorings of the \( k \) k -colored link by the topological \( k \) k -quandle.