Titlebook: Volume Conjecture for Knots; Hitoshi Murakami,Yoshiyuki Yokota Book 2018 The Author(s), under exclusive licence to Springer Nature Singapo

健谈

Volume Conjecture, invariant. The volume conjecture states that this function would grow exponentially with respect to . and its growth rate would give the simplicial volume of the knot complement. In this section we describe the volume conjecture and give proofs for the figure-eight knot and for the torus knot .(2, 2. + 1).

Pelvic-Floor

证明无罪

拾落穗

滴注

阻止

Generalizations of the Volume Conjecture, imaginary part of .. We expect the (.) Chern–Simons invariant to appear. Secondly, we refine the conjecture by considering more precise approximation of the colored Jones polynomial. We conjecture that the Reidemeister torsion would appear. Lastly, we perturb . in . slightly and see what happens to

强制性

Book 2018the knot complement. Here the colored Jones polynomial is a generalization of the celebrated Jones polynomial and is defined by using a so-called .R.-matrix that is associated with the .N.-dimensional representation of the Lie algebra sl(2;.C.). The volume conjecture was first stated by R. Kashaev i

凝乳

978-981-13-1149-9The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2018

Conflagration

macabre

R-Matrix, the Colored Jones Polynomial, and the Kashaev Invariant,In this chapter we give definitions of the colored Jones polynomial. To do that we use a braid presentation and a knot diagram. Kashaev’s invariant is obtained as a specialization of the colored Jones polynomial.