New Developments in the Theory of KnotsThis reprint volume focuses on recent developments in knot theory arising from mathematical physics, especially solvable lattice models, Yang-Baxter equation, quantum group and two dimensional conformal field theory. This volume is helpful to topologists and mathematical physicists because existing articles are scattered in journals of many different domains including Mathematics and Physics. This volume will give an excellent perspective on these new developments in Topology inspired by mathematical physics. |
Contents
Jones A Polynomial Invariant for Knots via von Neumann | 12 |
H Kauffman State Models and the Jones Polynomial | 162 |
Turaev The YangBaxter Equation and Invariants of Links | 175 |
A N Kirillov N Yu Reshetikhin Representations of the Algebra | 202 |
Rosso Groupes Quantiques et Modèles à Vertex de V Jones | 274 |
J Murakami The Parallel Version of Polynomial Invariants | 337 |
H Wenzl Hecke Algebras of Type and Subfactors | 420 |
J Birman and H Wenzl Braids Link Polynomials and a | 455 |
J Murakami The Kauffman Polynomial of Links | 479 |
S Yamada The Minimal Number of Seifert Circles Equals | 505 |
J Birman On the Jones Polynomial of Closed 3Braids | 527 |
K Murasugi Jones Polynomials of Alternating Links Trans | 535 |
K Murasugi Jones Polynomials and Classical Conjectures | 563 |
H Morton and H Short The 2Variable Polynomials of Cable | 582 |
H Murakami On the Derivatives of the Jones Polynomials | 594 |
Kauffman Statistical Mechanics and the Jones Polynomial | 778 |
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Common terms and phrases
3-braids Akutsu Alexander polynomial alternating link B₁ b₂ Birman braid group closed braid closure components compute Conformal Field Theory construction Corollary corresponding defined definition denote double points e₁ element equivalent Exactly Solvable Models factor Figure finite dimensional formula function Hecke algebras Hence homomorphism induction integer INVARIANTS OF LINKS IRF models irreducible representations isomorphic j₁ Jones polynomial Kauffman polynomial knots and links Lemma Lickorish linear link diagram link invariant link polynomials Markov trace Math matrix monodromy MURAKAMI MURASUGI Neumann algebras obtained Ocneanu oriented link PARALLEL VERSION parameter Phys polynomial invariant positive preprint proof of Theorem Proposition prove relations relative commutant satisfy Seifert circles statistical mechanics strings subalgebra subfactors symmetric tion topological trivial two-variable V. F. R. JONES V₁ vector vertex model vertex operators von Neumann algebras Wadati Wenzl Yang-Baxter equation Young diagram