Non-Fiction Books:

Volume Conjecture for Knots

Customer rating

Click to share your rating 0 ratings (0.0/5.0 average) Thanks for your vote!

Share this product

Volume Conjecture for Knots by Hitoshi Murakami
$161.99
In stock with supplier

The item is brand new and in-stock in with one of our preferred suppliers. The item will ship from the Mighty Ape warehouse within the timeframe shown below.

Usually ships within 2-3 weeks

Availability

Delivering to:

Estimated arrival:

  • Around 21-28 November using standard courier delivery

Description

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. 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 in terms of his own invariant defined by using the quantum dilogarithm. Later H. Murakami and J. Murakami proved that Kashaev's invariant is nothing but the N-dimensional colored Jones polynomial evaluated at the Nth root of unity. Then the volume conjecture turns out to be a conjecture that relates an algebraic object, the colored Jones polynomial, with a geometric object, the volume. In this book we start with the definition of the colored Jones polynomial by using braid presentations of knots. Then we state the volume conjecture and give a very elementary proof of the conjecture for the figure-eight knot following T. Ekholm. We then give a rough idea of the "proof", that is, we show why we think the conjecture is true at least in the case of hyperbolic knots by showing how the summation formula for the colored Jones polynomial "looks like" the hyperbolicity equations of the knot complement. We also describe a generalization of the volume conjecture that corresponds to a deformation of the complete hyperbolic structure of a knot complement. This generalization would relate the colored Jones polynomial of a knot to the volume and the Chern-Simons invariant of a certain representation of the fundamental group of the knot complement to the Lie group SL(2;C). We finish by mentioning further generalizations of the volume conjecture.
Release date NZ
August 27th, 2018
Country of Publication
Singapore
Edition
1st ed. 2018
Illustrations
18 Illustrations, color; 80 Illustrations, black and white; IX, 120 p. 98 illus., 18 illus. in color.
Imprint
Springer Verlag, Singapore
Pages
120
ISBN-13
9789811311499
Product ID
28125498

Customer reviews

Nobody has reviewed this product yet. You could be the first!

Write a Review

Marketplace listings

There are no Marketplace listings available for this product currently.
Already own it? Create a free listing and pay just 9% commission when it sells!

Sell Yours Here

Help & options

  • If you think we've made a mistake or omitted details, please send us your feedback. Send Feedback
  • If you have a question or problem with this product, visit our Help section. Get Help
  • Seen a lower price for this product elsewhere? We'll do our best to beat it. Request a better price
Filed under...

Buy this and earn 729 Banana Points