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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Geometric construction of spinors in orthogonal modular categories

Anna Beliakova

Algebraic & Geometric Topology 3 (2003) 969–992

arXiv: math.QA/0210237

Abstract

A geometric construction of 2–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 2–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 2000
Primary: 57M27
Secondary: 57R56
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Publication
Received: 29 January 2003
Revised: 14 August 2003
Accepted: 21 September 2003
Published: 4 October 2003
Authors
Anna Beliakova
Mathematisches Institut
Universität Basel
Rheinsprung 21
CH-4051 Basel
Switzerland