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KIAM Preprint № 52, Moscow, 2023
Authors: Aptekarev A.I.
Hyperbolic volume of 3-d manifolds, A-polynomials, numerical hypothesis testing
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.
Keywords:
knots, fundamental group of the complement of a knot, SL_2-representation, A-polynomials, WKB-asymptotics, q-difference equation, Volume Conjecture
Publication language: russian,  pages: 36
Research direction:
Mathematical problems and theory of numerical methods
Russian source text:
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About authors:
  • Aptekarev Alexander Ivanovich,  orcid.org/0000-0003-2777-3903KIAM RAS