Algebraic and Geometric Topology 3 (2003),
paper no. 32, pages 969-992.
Geometric construction of spinors in orthogonal modular categories
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.
Modular category, quantum invariant, Vassiliev--Kontsevich invariant, weight system
AMS subject classification.
Submitted: 29 January 2003.
(Revised: 14 August 2003.)
Accepted: 21 September 2003.
Published: 4 October 2003.
Notes on file formats
Mathematisches Institut, Universitaet Basel
Rheinsprung 21, CH-4051 Basel, Switzerland
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