Volume Conjecture

Murakami, Hitoshi; Yokota, Yoshiyuki

doi:10.1007/978-981-13-1150-5_3

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Introduction2

Proof Of Theorem 141

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2023

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(3 citation statements)

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“…We can see that the cohomological adjoint Reidemeister torsion equals and the Chern–Simons invariant is given by . See, for example, [29, Chapter 5] for the calculation of the adjoint Reidemeister torsion and the Chern–Simons invariant.…”

Section: Proof Of Theorem 14mentioning

confidence: 99%

“…Associated with u , we can define the Chern–Simons invariant and the cohomological adjoint Reidemeister torsion . See [29, Chapter 5] for example. Note that, in [29], we define the homological adjoint Reidemeister torsion (it is called the twisted Reidemeister torsion there).…”

Section: Introductionmentioning

confidence: 99%

“…See [29, Chapter 5] for example. Note that, in [29], we define the homological adjoint Reidemeister torsion (it is called the twisted Reidemeister torsion there). So we need to take its inverse to define the cohomological torsion.…”

Section: Introductionmentioning

confidence: 99%

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The colored Jones polynomial of the figure-eight knot and a quantum modularity

Murakami

2023

Can. J. Math.-J. Can. Math.

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We study the asymptotic behavior of the N-dimensional colored Jones polynomial of the figure-eight knot evaluated at $\exp \bigl ((u+2p\pi \sqrt {-1})/N\bigr )$ , where u is a small real number and p is a positive integer. We show that it is asymptotically equivalent to the product of the p-dimensional colored Jones polynomial evaluated at $\exp \bigl (4N\pi ^2/(u+2p\pi \sqrt {-1})\bigr )$ and a term that grows exponentially with growth rate determined by the Chern–Simons invariant. This indicates a quantum modularity of the colored Jones polynomial.

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