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

• Autore: Kauffman Louis H.
• Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]; ©1994
• Descrizione fisica: 1 online resource (308 pages) : illustrations
• Disciplina: 514/.224
• Soggetto topico: Knot theory; Three-manifolds (Topology); Invariants
• Soggetto non controllato: 3-manifold; Addition; Algorithm; Ambient isotopy; Axiom; Backslash; Barycentric subdivision; Bijection; Bipartite graph; Borromean rings; Boundary parallel; Bracket polynomial; Calculation; Canonical form; Cartesian product; Cobordism; Coefficient; Combination; Commutator; Complex conjugate; Computation; Connected component (graph theory); Connected sum; Cubic graph; Diagram (category theory); Dimension; Disjoint sets; Disjoint union; Elaboration; Embedding; Equation; Equivalence class; Explicit formula; Explicit formulae (L-function); Factorial; Fundamental group; Graph (discrete mathematics); Graph embedding; Handlebody; Homeomorphism; Homology (mathematics); Identity element; Intersection form (4-manifold); Inverse function; Jones polynomial; Kirby calculus; Knot theory; Line segment; Linear independence; Matching (graph theory); Mathematical physics; Mathematical proof; Mathematics; Maxima and minima; Monograph; Natural number; Network theory; Notation; Numerical analysis; Orientability; Orthogonality; Pairing; Pairwise; Parametrization; Parity (mathematics); Partition function (mathematics); Permutation; Poincaré conjecture; Polyhedron; Quantum group; Quantum invariant; Recoupling; Recursion; Reidemeister move; Result; Roger Penrose; Root of unity; Scientific notation; Sequence; Significant figures; Simultaneous equations; Smoothing; Special case; Sphere; Spin network; Summation; Symmetric group; Tetrahedron; The Geometry Center; Theorem; Theory; Three-dimensional space (mathematics); Time complexity; Tubular neighborhood; Two-dimensional space; Vector field; Vector space; Vertex (graph theory); Winding number; Writhe
• Persona (resp. second.): LinsSostenes
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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
• Sommario/riassunto: 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.
• Titolo autorizzato: Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134
• ISBN: 1-4008-8253-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910154743003321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; no. 134.