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Abstract
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A geometric construction of –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
–cohomological
refinements, respectively. The relation with the quantum group approach is
discussed.
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Keywords
modular category, quantum invariant, Vassiliev–Kontsevich
invariant, weight system
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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
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