The Resource An Introduction to Quantum and Vassiliev Knot Invariants, by David M. Jackson, Iain Moffatt, (electronic resource)

An Introduction to Quantum and Vassiliev Knot Invariants, by David M. Jackson, Iain Moffatt, (electronic resource)

Label
An Introduction to Quantum and Vassiliev Knot Invariants
Title
An Introduction to Quantum and Vassiliev Knot Invariants
Statement of responsibility
by David M. Jackson, Iain Moffatt
Creator
Contributor
Author
Author
Subject
Language
eng
Summary
This book provides an accessible introduction to knot theory, focussing on Vassiliev invariants, quantum knot invariants constructed via representations of quantum groups, and how these two apparently distinct theories come together through the Kontsevich invariant. Consisting of four parts, the book opens with an introduction to the fundamentals of knot theory, and to knot invariants such as the Jones polynomial. The second part introduces quantum invariants of knots, working constructively from first principles towards the construction of Reshetikhin-Turaev invariants and a description of how these arise through Drinfeld and Jimbo's quantum groups. Its third part offers an introduction to Vassiliev invariants, providing a careful account of how chord diagrams and Jacobi diagrams arise in the theory, and the role that Lie algebras play. The final part of the book introduces the Konstevich invariant. This is a universal quantum invariant and a universal Vassiliev invariant, and brings together these two seemingly different families of knot invariants. The book provides a detailed account of the construction of the Jones polynomial via the quantum groups attached to sl(2), the Vassiliev weight system arising from sl(2), and how these invariants come together through the Kontsevich invariant
Member of
http://library.link/vocab/creatorName
Jackson, David M
Dewey number
514.224
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • teY_PL9U3Ns
  • rHXQI95YIJE
LC call number
  • QA613-613.8
  • QA613.6-613.66
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Moffatt, Iain.
Series statement
CMS Books in Mathematics, Ouvrages de mathématiques de la SMC,
http://library.link/vocab/subjectName
  • Cell aggregation
  • Algebra
  • Manifolds and Cell Complexes (incl. Diff.Topology)
  • Non-associative Rings and Algebras
Label
An Introduction to Quantum and Vassiliev Knot Invariants, by David M. Jackson, Iain Moffatt, (electronic resource)
Instantiates
Publication
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Part I Basic Knot Theory -- Knots -- Knot and Link Invariants -- Framed Links -- Braids and the Braid Group -- Part II Quantum Knot Invariants -- R-Matrix Representations of Bn -- Knot Invariants through R-Matrix Representations of Bn -- Operator Invariants -- Ribbon Hopf Algebras -- Reshetikin-Turaev Invariants -- Part III Vassiliev Invarients -- The Fundamentals of Vassiliev Invariants -- Chord Diagrams -- Vassiliev Invariants of Framed Knots -- Jacobi Diagrams -- Lie Algebra Weight Systems -- Part IV The Kontsevich Invariant -- q-tangles -- Jacobi Diagrams on a 1-manifold -- A Construction of the Kontsevich Invariant -- Universality Properties of the Kontsevich Invariant -- Appendix A Background on Modules and Linear Algebra -- Appendix B Rewriting the Definition of Operator Invariants -- Appendix C Computations in Quasi-triangular Hopf Algebras -- Appendix D The Ribbon Hopf Algebra -- Appendix E A Proof of the Invariance of the Reshetikin-Turaev Invariants
Dimensions
unknown
Edition
1st ed. 2019.
Extent
1 online resource (425 pages)
Form of item
online
Isbn
9783030052133
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-030-05213-3
Sound
unknown sound
Specific material designation
remote
System control number
  • (CKB)4100000008103747
  • (MiAaPQ)EBC5771236
  • (DE-He213)978-3-030-05213-3
  • (EXLCZ)994100000008103747
Label
An Introduction to Quantum and Vassiliev Knot Invariants, by David M. Jackson, Iain Moffatt, (electronic resource)
Publication
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Part I Basic Knot Theory -- Knots -- Knot and Link Invariants -- Framed Links -- Braids and the Braid Group -- Part II Quantum Knot Invariants -- R-Matrix Representations of Bn -- Knot Invariants through R-Matrix Representations of Bn -- Operator Invariants -- Ribbon Hopf Algebras -- Reshetikin-Turaev Invariants -- Part III Vassiliev Invarients -- The Fundamentals of Vassiliev Invariants -- Chord Diagrams -- Vassiliev Invariants of Framed Knots -- Jacobi Diagrams -- Lie Algebra Weight Systems -- Part IV The Kontsevich Invariant -- q-tangles -- Jacobi Diagrams on a 1-manifold -- A Construction of the Kontsevich Invariant -- Universality Properties of the Kontsevich Invariant -- Appendix A Background on Modules and Linear Algebra -- Appendix B Rewriting the Definition of Operator Invariants -- Appendix C Computations in Quasi-triangular Hopf Algebras -- Appendix D The Ribbon Hopf Algebra -- Appendix E A Proof of the Invariance of the Reshetikin-Turaev Invariants
Dimensions
unknown
Edition
1st ed. 2019.
Extent
1 online resource (425 pages)
Form of item
online
Isbn
9783030052133
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
10.1007/978-3-030-05213-3
Sound
unknown sound
Specific material designation
remote
System control number
  • (CKB)4100000008103747
  • (MiAaPQ)EBC5771236
  • (DE-He213)978-3-030-05213-3
  • (EXLCZ)994100000008103747

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