Lectures in Knot Theory
portes grátis
Lectures in Knot Theory
An Exploration of Contemporary Topics
Ibarra, Dionne; Weeks, Deborah; Montoya-Vega, Gabriel; Bakshi, Rhea Palak; Przytycki, Jozef H.
Springer International Publishing AG
03/2024
520
Mole
Inglês
9783031400438
15 a 20 dias
Descrição não disponível.
1. History of Knot Theory From Ancient Times to Gauss and His Student Listing.- 2. History of Knot Theory From Gauss to Jones.- 3. FROM FOX 3-COLORING TO THE YANG-BAXTER OPERATOR.- 4. Lecture ?: Goeritz and Seifert Matrices.- 5. Chapter Heading.- 6. The HOMFLYPT and the 2-variable Kauffman Polynomial.- 7. Lecture 8: The Temperley - Lieb Algebra and Braid Groups.- 8. Lecture 9: Symmetrizers of Finite Groups and Jones-Wenzl Idempotents.- 9. Lecture 10: Plucking polynomial of rooted trees and its use in knot theory.- 10. Lecture 11: Basics of Skein Modules.- 11. Lecture 12: The Kauffman Bracket Skein Module.- 12. Lecture 13: The Kauffman Bracket Skein Module and Algebra of Surface I-bundles.- 13. Lecture 14: Multiplicative Structure of the Kauffman Bracket Skein Algebra of the Thickened T-Shirt.- 14. Spin Structure and the Framing Skein Module of Links in 3-Manifolds.- 15. Lecture 16: The Witten - Reshetikhin - Turaev Invariant of 3-manifolds.- 16. Lecture 19: Type A Gram determinant.-17. Lecture 18: Gram Determinants of Type B and Type M b.- 18. Lecture 19: Khovanov homology: a categorification of The Jones polynomial.- 19. Lecture 20: Long Exact Sequence of Khovanov Homology and Torsion.- 20. Lecture 21: Categorification of Skein Modules of Twisted I-bundles over surfaces.- Appendix A: Basics of 3-Dimensional Topology. -Appendix B: Surgery on Links in the 3-Sphere and Kirby's Calculus. -Glossary.- SOlutions.
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Knots and links;Fox colorings;Gram determinants;History of knots;Jones polynomial;Khovanov homology;Skein modules;Yang-Baxter operator
1. History of Knot Theory From Ancient Times to Gauss and His Student Listing.- 2. History of Knot Theory From Gauss to Jones.- 3. FROM FOX 3-COLORING TO THE YANG-BAXTER OPERATOR.- 4. Lecture ?: Goeritz and Seifert Matrices.- 5. Chapter Heading.- 6. The HOMFLYPT and the 2-variable Kauffman Polynomial.- 7. Lecture 8: The Temperley - Lieb Algebra and Braid Groups.- 8. Lecture 9: Symmetrizers of Finite Groups and Jones-Wenzl Idempotents.- 9. Lecture 10: Plucking polynomial of rooted trees and its use in knot theory.- 10. Lecture 11: Basics of Skein Modules.- 11. Lecture 12: The Kauffman Bracket Skein Module.- 12. Lecture 13: The Kauffman Bracket Skein Module and Algebra of Surface I-bundles.- 13. Lecture 14: Multiplicative Structure of the Kauffman Bracket Skein Algebra of the Thickened T-Shirt.- 14. Spin Structure and the Framing Skein Module of Links in 3-Manifolds.- 15. Lecture 16: The Witten - Reshetikhin - Turaev Invariant of 3-manifolds.- 16. Lecture 19: Type A Gram determinant.-17. Lecture 18: Gram Determinants of Type B and Type M b.- 18. Lecture 19: Khovanov homology: a categorification of The Jones polynomial.- 19. Lecture 20: Long Exact Sequence of Khovanov Homology and Torsion.- 20. Lecture 21: Categorification of Skein Modules of Twisted I-bundles over surfaces.- Appendix A: Basics of 3-Dimensional Topology. -Appendix B: Surgery on Links in the 3-Sphere and Kirby's Calculus. -Glossary.- SOlutions.
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