Volume Conjecture for Knots

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-mat...

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Bibliographische Detailangaben
1. Verfasser: Murakami, Hitoshi (VerfasserIn)
Format: Elektronisch E-Book
Sprache:Englisch
Veröffentlicht: Singapore : Springer Singapore , 2018.
Ausgabe:1st ed. 2018.
Schriftenreihe:SpringerBriefs in Mathematical Physics, 30
Schlagworte:
Mathematical physics.
Topology.
Hyperbolic geometry.
ISBN:9789811311505
ISSN:2197-1757 ;
Online-Zugang: Volltext
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Inhaltsangabe:
  • 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.

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