Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 /

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

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, hi...

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Superior document:Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
VerfasserIn:
Kauffman, Louis H.,
Lins, Sostenes,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2016]
©1994
Year of Publication:2016
Language:English
Series:Annals of Mathematics Studies ; 134
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Physical Description:1 online resource (312 p.) :; 1200 illus.
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spelling Kauffman, Louis H., author. aut http://id.loc.gov/vocabulary/relators/aut
Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 / Sostenes Lins, Louis H. Kauffman.
Princeton, NJ : Princeton University Press, [2016]
©1994
1 online resource (312 p.) : 1200 illus.
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
Annals of Mathematics Studies ; 134
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
restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star
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.
Issued also in print.
Mode of access: Internet via World Wide Web.
In English.
Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022)
Invariants.
Knot theory.
Three-manifolds (Topology).
MATHEMATICS / Topology. bisacsh
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.
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.
Lins, Sostenes, author. aut http://id.loc.gov/vocabulary/relators/aut
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496
print 9780691036403
https://doi.org/10.1515/9781400882533
https://www.degruyter.com/isbn/9781400882533
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language English
format eBook
author Kauffman, Louis H.,
Kauffman, Louis H.,
Lins, Sostenes,
spellingShingle Kauffman, Louis H.,
Kauffman, Louis H.,
Lins, Sostenes,
Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 /
Annals of Mathematics Studies ;
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
author_facet Kauffman, Louis H.,
Kauffman, Louis H.,
Lins, Sostenes,
Lins, Sostenes,
Lins, Sostenes,
author_variant l h k lh lhk
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s l sl
author_role VerfasserIn
VerfasserIn
VerfasserIn
author2 Lins, Sostenes,
Lins, Sostenes,
author2_variant s l sl
author2_role VerfasserIn
VerfasserIn
author_sort Kauffman, Louis H.,
title Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 /
title_full Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 / Sostenes Lins, Louis H. Kauffman.
title_fullStr Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 / Sostenes Lins, Louis H. Kauffman.
title_full_unstemmed Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 / Sostenes Lins, Louis H. Kauffman.
title_auth Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 /
title_alt 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
title_new Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 /
title_sort temperley-lieb recoupling theory and invariants of 3-manifolds (am-134), volume 134 /
series Annals of Mathematics Studies ;
series2 Annals of Mathematics Studies ;
publisher Princeton University Press,
publishDate 2016
physical 1 online resource (312 p.) : 1200 illus.
Issued also in print.
contents 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
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callnumber-subject QA - Mathematics
callnumber-label QA612
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illustrated Illustrated
dewey-hundreds 500 - Science
dewey-tens 510 - Mathematics
dewey-ones 514 - Topology
dewey-full 514/.224
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dewey-raw 514/.224
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doi_str_mv 10.1515/9781400882533
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Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999
is_hierarchy_title Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (AM-134), Volume 134 /
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tag="653" ind1=" " ind2=" "><subfield code="a">Root of unity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Scientific notation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Sequence.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Significant figures.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Simultaneous equations.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Smoothing.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Special case.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Sphere.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Spin network.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Summation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Symmetric group.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Tetrahedron.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">The Geometry Center.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Three-dimensional space (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Time complexity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Tubular neighborhood.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Two-dimensional space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Vector field.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Vector space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Vertex (graph theory).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Winding number.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Writhe.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Lins, Sostenes, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton Annals of Mathematics eBook-Package 1940-2020</subfield><subfield code="z">9783110494914</subfield><subfield code="o">ZDB-23-PMB</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De 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