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035   $a(MiAaPQ)EBC4738737
035   $a(DE-B1597)468002
035   $a(OCoLC)954123965
035   $a(OCoLC)990415133
035   $a(DE-B1597)9781400882533
035   $a(EXLCZ)993710000000631389
100   $a20190708d2016      fg 
101 0 $aeng
135   $aurcnu||||||||
181   $2rdacontent
182   $2rdamedia
183   $2rdacarrier
200 10$aTemperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 /$fLouis H. Kauffman, Sostenes Lins
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$d©1994
215   $a1 online resource (308 pages) $cillustrations
225 0 $aAnnals of Mathematics Studies ;$v315
311   $a0-691-03641-1 
311   $a0-691-03640-3 
320   $aIncludes bibliographical references and index.
327   $tFrontmatter -- $tContents -- $tChapter 1. Introduction -- $tChapter 2. Bracket Polynomial, Temperley-Lieb Algebra -- $tChapter 3. Jones-Wenzl Projectors -- $tChapter 4. The 3-Vertex -- $tChapter 5. Properties of Projectors and 3-Vertices -- $tChapter 6. ?-Evaluations -- $tChapter 7. Recoupling Theory Via Temperley-Lieb Algebra -- $tChapter 8. Chromatic Evaluations and the Tetrahedron -- $tChapter 9. A Summary of Recoupling Theory -- $tChapter 10. A 3-Manifold Invariant by State Summation -- $tChapter 11. The Shadow World -- $tChapter 12. The Witten-Reshetikhin- Turaev Invariant -- $tChapter 13. Blinks ? 3-Gems: Recognizing 3-Manifolds -- $tChapter 14. Tables of Quantum Invariants -- $tBibliography -- $tIndex
330   $aThis book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants. The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra. This recoupling theory is a q-deformation of the SU(2) spin networks of Roger Penrose. The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the Kirillov-Reshetikhin shadow world, leading to expressions for all the invariants in terms of state summations on 2-cell complexes. Extensive tables of the invariants are included. Manifolds in these tables are recognized by surgery presentations and by means of 3-gems (graph encoded 3-manifolds) in an approach pioneered by Sostenes Lins. The appendices include information about gems, examples of distinct manifolds with the same invariants, and applications to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds.
410  0$aAnnals of mathematics studies ;$vno. 134.
606   $aKnot theory
606   $aThree-manifolds (Topology)
606   $aInvariants
610   $a3-manifold.
610   $aAddition.
610   $aAlgorithm.
610   $aAmbient isotopy.
610   $aAxiom.
610   $aBackslash.
610   $aBarycentric subdivision.
610   $aBijection.
610   $aBipartite graph.
610   $aBorromean rings.
610   $aBoundary parallel.
610   $aBracket polynomial.
610   $aCalculation.
610   $aCanonical form.
610   $aCartesian product.
610   $aCobordism.
610   $aCoefficient.
610   $aCombination.
610   $aCommutator.
610   $aComplex conjugate.
610   $aComputation.
610   $aConnected component (graph theory).
610   $aConnected sum.
610   $aCubic graph.
610   $aDiagram (category theory).
610   $aDimension.
610   $aDisjoint sets.
610   $aDisjoint union.
610   $aElaboration.
610   $aEmbedding.
610   $aEquation.
610   $aEquivalence class.
610   $aExplicit formula.
610   $aExplicit formulae (L-function).
610   $aFactorial.
610   $aFundamental group.
610   $aGraph (discrete mathematics).
610   $aGraph embedding.
610   $aHandlebody.
610   $aHomeomorphism.
610   $aHomology (mathematics).
610   $aIdentity element.
610   $aIntersection form (4-manifold).
610   $aInverse function.
610   $aJones polynomial.
610   $aKirby calculus.
610   $aKnot theory.
610   $aLine segment.
610   $aLinear independence.
610   $aMatching (graph theory).
610   $aMathematical physics.
610   $aMathematical proof.
610   $aMathematics.
610   $aMaxima and minima.
610   $aMonograph.
610   $aNatural number.
610   $aNetwork theory.
610   $aNotation.
610   $aNumerical analysis.
610   $aOrientability.
610   $aOrthogonality.
610   $aPairing.
610   $aPairwise.
610   $aParametrization.
610   $aParity (mathematics).
610   $aPartition function (mathematics).
610   $aPermutation.
610   $aPoincaré conjecture.
610   $aPolyhedron.
610   $aQuantum group.
610   $aQuantum invariant.
610   $aRecoupling.
610   $aRecursion.
610   $aReidemeister move.
610   $aResult.
610   $aRoger Penrose.
610   $aRoot of unity.
610   $aScientific notation.
610   $aSequence.
610   $aSignificant figures.
610   $aSimultaneous equations.
610   $aSmoothing.
610   $aSpecial case.
610   $aSphere.
610   $aSpin network.
610   $aSummation.
610   $aSymmetric group.
610   $aTetrahedron.
610   $aThe Geometry Center.
610   $aTheorem.
610   $aTheory.
610   $aThree-dimensional space (mathematics).
610   $aTime complexity.
610   $aTubular neighborhood.
610   $aTwo-dimensional space.
610   $aVector field.
610   $aVector space.
610   $aVertex (graph theory).
610   $aWinding number.
610   $aWrithe.
615  0$aKnot theory.
615  0$aThree-manifolds (Topology)
615  0$aInvariants.
676   $a514/.224
700   $aKauffman$b Louis H., $057757
702   $aLins$b Sostenes, 
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154743003321
996   $aTemperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134$92785665
997   $aUNINA