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Quantum Invariants of Knots and 3-Manifolds

- V. Turaev
- Physics, Mathematics
- 1 July 1994

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… Expand

Invariants of 3-manifolds via link polynomials and quantum groups

- N. Reshetikhin, V. Turaev
- Mathematics
- 1 December 1991

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… Expand

Ribbon graphs and their invaraints derived from quantum groups

- N. Reshetikhin, V. Turaev
- Mathematics
- 1990

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… Expand

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… Expand

The Yang-Baxter equation and invariants of links

- V. Turaev
- Mathematics
- 1 October 1988

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

- I. Frenkel, V. Turaev
- Mathematics
- 1997

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… Expand

Introduction to Combinatorial Torsions

- V. Turaev
- Mathematics
- 1 March 2001

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… Expand

Reidemeister torsion in knot theory

- V. Turaev
- Mathematics
- 28 February 1986

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… Expand

Skein quantization of Poisson algebras of loops on surfaces

- V. Turaev
- Mathematics
- 1991

© 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.… Expand

Homotopy field theory in dimension 3 and crossed group-categories

- V. Turaev
- Mathematics
- 31 May 2000

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… Expand

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