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We briefly review \(SL(2,\mathbb {C})\) -Chern-Simons partition function Z[M] on a closed three-manifold \(\mathcal {M}\) obtained from Dehn fillings on a link complement \(\textbf{S}^3\backslash {L}\) . We focus on links L which are connected sum of a knot \(\mathcal K\) with a Hopf link H ( \( L= K\# H\) ). Using SnapPy [1], we deduce the choice of the Dehn fillings which gives the imaginary part of the leading order term in the perturbative expansion of Z[M] to be the hyperbolic volume of the knot K. We have given explicit results for knot \( K= 4_1\) .

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State Integral Partition Function of Knots, Links and Dehn Surgery

  • 会议论文

  • 发表日期：

    2025年

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  • Aditya Dwivedi,
  • Bhabani Prasad Mandal

摘要

We briefly review \(SL(2,\mathbb {C})\) -Chern-Simons partition function Z[M] on a closed three-manifold \(\mathcal {M}\) obtained from Dehn fillings on a link complement \(\textbf{S}^3\backslash {L}\) . We focus on links L which are connected sum of a knot \(\mathcal K\) with a Hopf link H ( \( L= K\# H\) ). Using SnapPy [1], we deduce the choice of the Dehn fillings which gives the imaginary part of the leading order term in the perturbative expansion of Z[M] to be the hyperbolic volume of the knot K. We have given explicit results for knot \( K= 4_1\) .