Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 / / Sostenes Lins, Louis H. Kauffman.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Kauffman, Louis H.,; Lins, Sostenes,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2016]; ©1994
• Year of Publication: 2016
• Language: English
• Series: Annals of Mathematics Studies ; 134
• Physical Description: 1 online resource (312 p.) :; 1200 illus.
• Other title: Frontmatter --; Contents --; Chapter 1. Introduction --; Chapter 2. Bracket Polynomial, Temperley-Lieb Algebra --; Chapter 3. Jones-Wenzl Projectors --; Chapter 4. The 3-Vertex --; Chapter 5. Properties of Projectors and 3-Vertices --; Chapter 6. θ-Evaluations --; Chapter 7. Recoupling Theory Via Temperley-Lieb Algebra --; Chapter 8. Chromatic Evaluations and the Tetrahedron --; Chapter 9. A Summary of Recoupling Theory --; Chapter 10. A 3-Manifold Invariant by State Summation --; Chapter 11. The Shadow World --; Chapter 12. The Witten-Reshetikhin- Turaev Invariant --; Chapter 13. Blinks ↦ 3-Gems: Recognizing 3-Manifolds --; Chapter 14. Tables of Quantum Invariants --; Bibliography --; Index
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9781400882533; 9783110494914; 9783110442496
• DOI: 10.1515/9781400882533
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Sostenes Lins, Louis H. Kauffman.

This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants. The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra. This recoupling theory is a q-deformation of the SU(2) spin networks of Roger Penrose. The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the Kirillov-Reshetikhin shadow world, leading to expressions for all the invariants in terms of state summations on 2-cell complexes. Extensive tables of the invariants are included. Manifolds in these tables are recognized by surgery presentations and by means of 3-gems (graph encoded 3-manifolds) in an approach pioneered by Sostenes Lins. The appendices include information about gems, examples of distinct manifolds with the same invariants, and applications to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds.