TY - BOOK ID - 2536278 TI - Temperley-Lieb recoupling theory and invariants of 3-manifolds AU - Kauffman, Louis H. AU - Lins, Sóstenes L. PY - 1994 VL - 134 SN - 0691036411 0691036403 1400882532 9780691036403 9780691036410 PB - Princeton, N.J. Princeton University Press DB - UniCat KW - Drie-menigvuldigheden (Topologie) KW - Knopentheorie KW - Knot theory KW - Noeuds [Theorie des ] KW - Three-manifolds (Topology) KW - Trois-variétés (Topologie) KW - Knot theory. KW - Algebraic topology KW - Invariants KW - Mathematics KW - Invariants (Mathematics) KW - Invariants. KW - 3-manifolds (Topology) KW - Manifolds, Three dimensional (Topology) KW - Three-dimensional manifolds (Topology) KW - Low-dimensional topology KW - Topological manifolds KW - Knots (Topology) KW - 3-manifold. KW - Addition. KW - Algorithm. KW - Ambient isotopy. KW - Axiom. KW - Backslash. KW - Barycentric subdivision. KW - Bijection. KW - Bipartite graph. KW - Borromean rings. KW - Boundary parallel. KW - Bracket polynomial. KW - Calculation. KW - Canonical form. KW - Cartesian product. KW - Cobordism. KW - Coefficient. KW - Combination. KW - Commutator. KW - Complex conjugate. KW - Computation. KW - Connected component (graph theory). KW - Connected sum. KW - Cubic graph. KW - Diagram (category theory). KW - Dimension. KW - Disjoint sets. KW - Disjoint union. KW - Elaboration. KW - Embedding. KW - Equation. KW - Equivalence class. KW - Explicit formula. KW - Explicit formulae (L-function). KW - Factorial. KW - Fundamental group. KW - Graph (discrete mathematics). KW - Graph embedding. KW - Handlebody. KW - Homeomorphism. KW - Homology (mathematics). KW - Identity element. KW - Intersection form (4-manifold). KW - Inverse function. KW - Jones polynomial. KW - Kirby calculus. KW - Line segment. KW - Linear independence. KW - Matching (graph theory). KW - Mathematical physics. KW - Mathematical proof. KW - Mathematics. KW - Maxima and minima. KW - Monograph. KW - Natural number. KW - Network theory. KW - Notation. KW - Numerical analysis. KW - Orientability. KW - Orthogonality. KW - Pairing. KW - Pairwise. KW - Parametrization. KW - Parity (mathematics). KW - Partition function (mathematics). KW - Permutation. KW - Poincaré conjecture. KW - Polyhedron. KW - Quantum group. KW - Quantum invariant. KW - Recoupling. KW - Recursion. KW - Reidemeister move. KW - Result. KW - Roger Penrose. KW - Root of unity. KW - Scientific notation. KW - Sequence. KW - Significant figures. KW - Simultaneous equations. KW - Smoothing. KW - Special case. KW - Sphere. KW - Spin network. KW - Summation. KW - Symmetric group. KW - Tetrahedron. KW - The Geometry Center. KW - Theorem. KW - Theory. KW - Three-dimensional space (mathematics). KW - Time complexity. KW - Tubular neighborhood. KW - Two-dimensional space. KW - Vector field. KW - Vector space. KW - Vertex (graph theory). KW - Winding number. KW - Writhe. UR - https://www.unicat.be/uniCat?func=search&query=sysid:2536278 AB - 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. ER -