Volume Conjecture for Knots

ISBN-13: 9789811311499 / Angielski / Miękka / 2018 / 120 str.

Hitoshi Murakami; Yoshiyuki Yokota

Opis

The volume conjecture states that a certain limit of the colored Jones polynomial of a knot in the three-dimensional sphere would give the volume of the knot complement.

Recenzje

"This book is a very nice account of the volume conjecture for knots, a fascinating question that relates quantum invariants to hyperbolic geometry. ... The book contains a lot of explicit examples and computations. I expect it will become a classical reference in the field." (Joan Porti, zbMath 1410.57001, 2019)

Spis treści

1. Preliminaries (knots and links, braids, hyperbolic geometry).- 2. R-matrix, the Kashaev invariant and the colored Jones polynomimal.- 3. Volume conjecture.- 4. Triangulation of a knot complement and hyperbolicity equation.- 5. Idea of the “proof”.- 6. Representations of a knot group into SL(2;C) and their Chern-Simons invariant.- 7. Generalization of the volume conjecture.