8 citations · 22 across the 4 of their papers we have counts for
11 papers
Problems on invariants of knots and 3-manifolds
J. E. Andersen, N. Askitas, D. Bar-Natan +57
This is a list of open problems on invariants of knots and 3-manifolds with expositions of their history, background, significance, or importance. This list was made by editing ope…
Asymptotic behaviors of the colored Jones polynomials of a torus knot
Hitoshi Murakami
We study the asymptotic behaviors of the colored Jones polynomials of torus knots. Contrary to the works by R. Kashaev, O. Tirkkonen, Y. Yokota, and the author, they do not seem to…
Some limits of the colored Jones polynomials of the figure-eight knot
Hitoshi Murakami
We will study the asymptotic behaviors of the colored Jones polynomials of the figure-eight knot. In particular we will show that for certain limits we obtain the volumes of the co…
Mahler measure of the colored Jones polynomial and the volume conjecture
Hitoshi Murakami
In this note, I will discuss a possible relation between the Mahler measure of the colored Jones polynomial and the volume conjecture. In particular, I will study the colored Jones…
Kashaev's conjecture and the Chern-Simons invariants of knots and links
Hitoshi Murakami, Jun Murakami, Miyuki Okamoto +2
R.M. Kashaev conjectured that the asymptotic behavior of his link invariant, which equals the colored Jones polynomial evaluated at a root of unity, determines the hyperbolic volum…
Optimistic calculations about the Witten--Reshetikhin--Turaev invariants of closed three-manifolds obtained from the figure-eight knot by integral Dehn surgeries
Hitoshi Murakami
I calculate optimistically asymptotic behaviors of the WRT SU(2) invariants for the three-manifolds obtained from the figure-eight knot by p-surgeries with p=0,1,2,...,10, from whi…