Volume conjecture for knots. (2018)

• Record Type: Book
• Further Information: Note: Hitoshi Murakami, Yoshiyuki Yokota.
• Authors: Murakami, Hitoshi; Yokota, Yoshiyuki
• Contents: Intro; Preface; Contents; Acronyms; 1 Preliminaries; 1.1 Knot; 1.2 Satellite; 1.3 Braid; 2 R-Matrix, the Colored Jones Polynomial, and the Kashaev Invariant; 2.1 A Link Invariant Derived from a Yang-Baxter Operator; 2.1.1 Yang-Baxter Operator; 2.1.2 Colored Jones Polynomial; 2.1.3 Kashaev's R-Matrix; 2.1.4 Example of Calculation; 2.2 Colored Jones Polynomial via the Kauffman Bracket; 2.2.1 Kauffman Bracket; 2.2.2 Example of Calculation; 3 Volume Conjecture; 3.1 Volume Conjecture; 3.2 Figure-Eight Knot; 3.3 Torus Knot; 4 Idea of ``Proof''; 4.1 Algebraic Part; 4.2 Analytic Part. 4.2.1 Integral Expression4.2.2 Potential Function; 4.2.3 Saddle Point Method; 4.2.4 Remaining Tasks; 4.3 Geometric Part; 4.3.1 Ideal Triangulation; 4.3.2 Cusp Triangulation; 4.3.3 Hyperbolicity Equations; 4.3.4 Complex Volumes; 5 Representations of a Knot Group, Their Chern-Simons Invariants, and Their Reidemeister Torsions; 5.1 Representations of a Knot Group; 5.1.1 Presentation; 5.1.2 Representation; 5.2 The Chern-Simons Invariant; 5.2.1 Definition; 5.2.2 How to Calculate; 5.3 Twisted SL(2; C) Reidemeister Torsion; 5.3.1 Definition; 5.3.2 How to Calculate. 6 Generalizations of the Volume Conjecture6.1 Complexification; 6.2 Refinement; 6.2.1 Figure-Eight Knot; 6.2.2 Torus Knot; 6.3 Parametrization; 6.3.1 Torus Knot; 6.3.2 Figure-Eight Knot; 6.4 Miscellaneous Results; 6.5 Final Remarks; References; Index.
• Publisher Details: Singapore : Springer
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 514/.2242; Knot theory; MATHEMATICS -- Topology; Knot theory; Mathematical Physics; Topology; Hyperbolic Geometry; Electronic books
• Languages: English
• ISBNs: 9789811311505; 9811311501; 9789811311512
• Related ISBNs: 9789811311499; 9811311498; 981131151X
• Notes: Note: Includes bibliographical references and index.; Note: Online resource; title from PDF title page (SpringerLink, viewed August 20, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.