Algebraic & Geometric Topology 3 (2003) 969–992

DOI: 10.2140/agt.2003.3.969

arXiv: math.QA/0210237

Abstract

A geometric construction of Z₂–graded odd and even orthogonal modular categories is given. Their 0–graded parts coincide with categories previously obtained by Blanchet and the author from the category of tangles modulo the Kauffman skein relations. Quantum dimensions and twist coefficients of 1–graded simple objects (spinors) are calculated. We show that invariants coming from our odd and even orthogonal modular categories admit spin and Z₂–cohomological refinements, respectively. The relation with the quantum group approach is discussed.

Keywords

modular category, quantum invariant, Vassiliev–Kontsevich invariant, weight system

Mathematical Subject Classification

Primary: 57M27

Secondary: 57R56

References

Forward citations

Publication

Received: 29 January 2003
Revised: 14 August 2003
Accepted: 21 September 2003
Published: 4 October 2003

Authors