Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds
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3-manifold
A01=Louis H. Kauffman
A01=Sostenes Lins
Addition
Ambient isotopy
Author_Louis H. Kauffman
Author_Sostenes Lins
Axiom
Barycentric subdivision
Bijection
Bipartite graph
Borromean rings
Bracket polynomial
Calculation
Cartesian product
Category=PBF
Category=PBPD
Cobordism
Coefficient
Combination
Commutator
Complex conjugate
Computation
Connected component (graph theory)
Connected sum
Diagram (category theory)
Dimension
Disjoint sets
Disjoint union
Embedding
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Equivalence class
Explicit formula
Explicit formulae (L-function)
Fundamental group
Graph (discrete mathematics)
Handlebody
Homeomorphism
Homology (mathematics)
Identity element
Intersection form (4-manifold)
Inverse function
Jones polynomial
Kirby calculus
Knot theory
Line segment
Matching (graph theory)
Mathematical physics
Mathematical proof
Mathematics
Maxima and minima
Notation
Orthogonality
Parametrization
Parity (mathematics)
Partition function (mathematics)
Permutation
Poincare conjecture
Quantum group
Quantum invariant
Recoupling
Reidemeister move
Root of unity
Scientific notation
Sequence
Simultaneous equations
Smoothing
Special case
Spin network
Summation
Tetrahedron
Theorem
Theory
Three-dimensional space (mathematics)
Winding number
Writhe
Product details
- ISBN 9780691036403
- Weight: 425g
- Dimensions: 197 x 254mm
- Publication Date: 25 Jul 1994
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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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.
Louis H. Kauffman is Professor of Mathematics at the University of Illinois, Chicago. Sostenes Lins is Professor of Mathematics at the Universidade Federal de Pernambuco in Recife, Brazil.
