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Quantum Invariants of Knots and 3-Manifolds
This monograph, now in its second revised edition, provides a systematic treatment of topological quantum field theories in three dimensions, inspired by the discovery of the Jones polynomial of
Invariants of 3-manifolds via link polynomials and quantum groups
The aim of this paper is to construct new topological invariants of compact oriented 3-manifolds and of framed links in such manifolds. Our invariant of (a link in) a closed oriented 3-manifold is a
Ribbon graphs and their invaraints derived from quantum groups
The generalization of Jones polynomial of links to the case of graphs inR3 is presented. It is constructed as the functor from the category of graphs to the category of representations of the quantum
State sum invariants of 3 manifolds and quantum 6j symbols
IN THE 1980s the topology of low dimensional manifolds has experienced the most remarkable intervention of ideas developed in rather distant areas of mathematics. In the 4dimensional topology this
The Yang-Baxter equation and invariants of links
On considere le fait que l'on peut construire des invariants d'isotopie P et F pour des liens en utilisant certaines solutions des equations de Yang Baxter
Elliptic solutions of the Yang-Baxter equation and modular hypergeometric functions
Various results in algebra, analysis, and geometry can be generalized by replacing the ordinary numbers (integer, real or complex) by their trigonometric analogues. For x ∈ ℂ, the trigonometric
Introduction to Combinatorial Torsions
I Algebraic Theory of Torsions.- 1 Torsion of chain complexes.- 2 Computation of the torsion.- 3 Generalizations and functoriality of the torsion.- 4 Homological computation of the torsion.- II
Reidemeister torsion in knot theory
CONTENTS Introduction § 0. Preliminary material § 1. Milnor torsion and the Alexander polynomial § 2. Proof of Theorems 1.1.1, 1.1.2, and 1.1.3 § 3. Refined torsion and the refined Alexander function
Skein quantization of Poisson algebras of loops on surfaces
© Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1991, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www.
Homotopy field theory in dimension 3 and crossed group-categories
A 3-dimensional homotopy quantum field theory (HQFT) can be described as a TQFT for surfaces and 3-cobordisms endowed with homotopy classes of maps into a given space. For a group $\pi$, we introduce