Volume of hyperbolic 3-manifolds

introduction

volume is an important invariant of hyperbolic 3-manifold
big open problem Kashaev's volume conjecture
three simple hyperbolic knots
- \(4_{1}\) figure 8 knot
- \(5_{2}\)
- \(6_{1}\), \(6_{1}\), \(6_{1}\)
A theorem of Jorgensen and Thurston implies that the volume of a hyperbolic 3-manifold is bounded below by a linear function of its Heegaard genus

Steven Finch, Volumes of Hyperbolic 3-Manifolds, September 5, 2004 http://algo.inria.fr/csolve/hyp.pdf

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Alexander Goncharov, Volumes of Hyperbolic Manifolds and Mixed Tate Motives, 1999
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Don Zagier, Hyperbolic manifolds and special values of Dedekind zeta-functions, Inventiones Mathematicae, Volume 83, Number 2 / 1986년 6월
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