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.

Keywords

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

Mathematical Subject Classification 2000

Primary: 57M27

Secondary: 57R56

References

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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

Volume 3, issue 2 (2003)

Anna Beliakova