WebMar 24, 2024 · The Alexander polynomial is a knot invariant discovered in 1923 by J. W. Alexander (Alexander 1928). The Alexander polynomial remained the only known knot polynomial until the Jones polynomial was discovered in 1984. Unlike the Alexander polynomial, the more powerful Jones polynomial does, in most cases, distinguish … Webequivalent knots, invariants will stay constant, meaning an invariant found in one gure-eight knot will be the same in another gure-eight knot. In other words, an invariant calculated from one knot will be calculated to be the same for equivalent knots. If two knots have two distinct invariant values, those two knots must be nonequivalent.
3-coloring and other elementary invariants of knots
WebMay 5, 2024 · This chapter introduces the concept of a knot invariant. Knot invariants are mathematical devices for determining when knots and links are inequivalent. It discusses … WebJan 15, 2012 · Although, in my opinion, it is strongly influenced by Rolfsen's Knots and Links, Prasolov and Sossinsky's Knots, Links, Braids and 3-Manifolds: An Introduction to the New Invariants in Low-Dimensional Topology is nice because there are references to recent articles in the appendices of each section. number bonds to 20 clipart
[hep-th/9912123] Knot Invariants and Topological Strings - arXiv.org
WebThis 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. WebMar 24, 2011 · 1. Knots and their relatives 2. Knot invariants 3. Finite type invariants 4. Chord diagrams 5. Jacobi diagrams 6. Lie algebra weight systems 7. Algebra of 3-graphs 8. The Kontsevich integral 9. Framed knots and cabling operations 10. The Drinfeld associator 11. The Kontsevich integral: advanced features 12. Braids and string links 13. Gauss … Webknots and the Arf invariant. Key concepts are related in easy-to-remember terms, and numerous helpful diagrams appear throughout the text. The author has provided a new supplement, entitled "Remarks on Formal Knot Theory," as well as his article, "New Invariants in the Theory of Knots," first published in The American Mathematical Monthly ... number bonds to 20 free printable worksheets