Algebraic and Geometric Topology 3 (2003), paper no. 32, pages 969-992.

Geometric construction of spinors in orthogonal modular categories

Anna Beliakova

Abstract. A geometric construction of Z_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 Z_2-cohomological refinements, respectively. The relation with the quantum group approach is discussed.

Keywords. Modular category, quantum invariant, Vassiliev--Kontsevich invariant, weight system

AMS subject classification. Primary: 57M27. Secondary: 57R56.

DOI: 10.2140/agt.2003.3.969

E-print: arXiv:math.QA/0210237

Submitted: 29 January 2003. (Revised: 14 August 2003.) Accepted: 21 September 2003. Published: 4 October 2003.

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Anna Beliakova
Mathematisches Institut, Universitaet Basel
Rheinsprung 21, CH-4051 Basel, Switzerland

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