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<p>We realize a homological block of a knot complement in <i>S</i><sup>3</sup> for <i>G</i><sub><i>ℂ</i></sub> = SL(2, <i>ℂ</i>) as a half-index of a 3d <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">N</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{N} \)</EquationSource> </InlineEquation> = 2 theory via an expression of the homological block as an inverted Habiro series by working out some examples, which we expect to extend to general knots. Also, by choosing a certain set of poles in the integral expression of the half-index, we obtain the colored Jones polynomial.</p>

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3d-3d correspondence and abelian flat connection

  • 期刊论文

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  • 发表日期：

    2026年7月9日

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  • Hee-Joong Chung

摘要

We realize a homological block of a knot complement in S3 for Gℂ = SL(2, ℂ) as a half-index of a 3d N \( \mathcal{N} \) = 2 theory via an expression of the homological block as an inverted Habiro series by working out some examples, which we expect to extend to general knots. Also, by choosing a certain set of poles in the integral expression of the half-index, we obtain the colored Jones polynomial.