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Abstract <p>We continue our study of the connections between the hyperbolic volume of the complement of a knot in the three dimensional sphere with topological invariants of this knot. This time we pay attention to <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(A(M,L)\)</EquationSource> <!--LobJMat2561044Aptekarev-m5--> </InlineEquation> parametrization for the affine variety with casp, produced by a knot (so-called <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(A\)</EquationSource> <!--LobJMat2561044Aptekarev-m6--> </InlineEquation>-polynomials). Then, using the known expressions of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(A\)</EquationSource> <!--LobJMat2561044Aptekarev-m7--> </InlineEquation>-polynomials for number of knots we present results of the numerical tests for the conjectures on asymptotics of solutions of <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(q\)</EquationSource> <!--LobJMat2561044Aptekarev-m8--> </InlineEquation>-difference equations connected with the hyperbolic volume of these knots.</p>

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Hyperbolic Volume of 3-\(\boldsymbol{d}\) Manifolds, \(\boldsymbol{A}\)-Polynomials, Numerical Testing of Hypotheses

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • A. I. Aptekarev

摘要

Abstract

We continue our study of the connections between the hyperbolic volume of the complement of a knot in the three dimensional sphere with topological invariants of this knot. This time we pay attention to \(A(M,L)\) parametrization for the affine variety with casp, produced by a knot (so-called \(A\) -polynomials). Then, using the known expressions of \(A\) -polynomials for number of knots we present results of the numerical tests for the conjectures on asymptotics of solutions of \(q\) -difference equations connected with the hyperbolic volume of these knots.