Modular categories and 3-manifold invariants

Journal Article · Mon Jun 01 00:00:00 EDT 1992 · International Journal of Modern Physics B; (United States)

DOI:https://doi.org/10.1142/S0217979292000876· OSTI ID:7173037

Tureav, V G ^[1]

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1. URA-CNRS, Dept. de Mathematique, Univ. Louis Pasteur, 7 rue Rene Descartes, 67084 Strasbourg Cedex (FR)

The aim of this paper is to give a concise introduction to the theory of knot invariants and 3-manifold invariants which generalize the Jones polynomial and which may be considered as a mathematical version of the Witten invariants. Such a theory was introduced by N. Reshetikhin and the author on the ground of the theory of quantum groups. here we use more general algebraic objects, specifically, ribbon and modular categories. Such categories in particular arise as the categories of representations of quantum groups. The notion of modular category, interesting in itself, is closely related to the notion of modular tensor category in the sense of G. Moore and N. Seiberg. For simplicity we restrict ourselves in this paper to the case of closed 3-manifolds.

• OSTI ID: 7173037
• Journal Information: International Journal of Modern Physics B; (United States), Vol. 6:11-12; ISSN 0217-9792
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
MATHEMATICAL MANIFOLDS
SYMMETRY GROUPS
INVARIANCE PRINCIPLES
POLYNOMIALS
QUANTUM MECHANICS
TENSORS
FUNCTIONS
MECHANICS
661100* - Classical & Quantum Mechanics- (1992-)
662110 - General Theory of Particles & Fields- Theory of Fields & Strings- (1992-)