06901nam 22017415 450 991015474300332120190708092533.01-4008-8253-210.1515/9781400882533(CKB)3710000000631389(MiAaPQ)EBC4738737(DE-B1597)468002(OCoLC)954123965(OCoLC)990415133(DE-B1597)9781400882533(EXLCZ)99371000000063138920190708d2016 fg engurcnu||||||||rdacontentrdamediardacarrierTemperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 /Louis H. Kauffman, Sostenes LinsPrinceton, NJ : Princeton University Press, [2016]©19941 online resource (308 pages) illustrationsAnnals of Mathematics Studies ;3150-691-03641-1 0-691-03640-3 Includes bibliographical references and index.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 -- IndexThis 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.Annals of mathematics studies ;no. 134.Knot theoryThree-manifolds (Topology)Invariants3-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.Knot theory.Three-manifolds (Topology)Invariants.514/.224Kauffman Louis H., 57757Lins Sostenes, DE-B1597DE-B1597BOOK9910154743003321Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 1342785665UNINA