Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
612-822-4611

  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Volume Conjecture for Knots

Volume Conjecture for Knots

Murakami, Hitoshi
Yokota, Yoshiyuki

Paperback

Series: Springerbriefs in Mathematical Physics, Book 30

General MathematicsGeometryPhysics

ISBN10: 9811311498
ISBN13: 9789811311499
Publisher: Springer Nature
Published: Aug 27 2018
Pages: 120
Weight: 0.43
Height: 0.28 Width: 6.14 Depth: 9.21
Language: English

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.

Also in

Physics

View All