scholarly journals Quantum Groups, Integrable Statistical Models and Knot Theory

10.1142/2093 ◽  
1993 ◽  
Keyword(s):  
Quantum Groups ◽  
Statistical Models ◽  
Knot Theory

THE MULTIVARIABLE ALEXANDER POLYNOMIAL AND MODERN KNOT THEORY

1992 ◽  
Vol 06 (11n12) ◽  
pp. 1857-1869
Author(s):  
H. SALEUR
Keyword(s):  
Quantum Groups ◽  
Knot Theory ◽  
Alexander Polynomial ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Link Invariant ◽  
Topological Quantum ◽  
Topological Quantum Field Theories

This note is a summary of several recent works (by the author and collaborators) that study the Conway-Alexander link invariant in the light of quantum groups and topological quantum field theories. Their purpose is to understand connections between “modern” knot theory and more classical topological concepts.

GAUSS CODES, QUANTUM GROUPS AND RIBBON HOPF ALGEBRAS

1993 ◽  
Vol 05 (04) ◽  
pp. 735-773 ◽  
Author(s):  
LOUIS H. KAUFFMAN
Keyword(s):  
Quantum Groups ◽  
Hopf Algebras ◽  
Knot Theory ◽  
Link Invariants ◽  
Finite Dimensional ◽  
Quantum Link

By relating the diagrammatic foundations of knot theory with the structure of abstract tensors, quantum groups and ribbon Hopf algebras, specific expressions are derived for quantum link invariants. These expressions, when applied to the case of finite dimensional unimodular ribbon Hopf algebras, give rise to invariants of 3-manifolds.

Sign in / Sign up

Export Citation Format

Share Document