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Geometric construction of spinors in orthogonal modular categories


Beliakova, A (2003). Geometric construction of spinors in orthogonal modular categories. Algebraic & Geometric Topology, 3:969-992 (electronic).

Abstract

A geometric construction of Z2–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 Z2–cohomological refinements, respectively. The relation with the quantum group approach is discussed.

Abstract

A geometric construction of Z2–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 Z2–cohomological refinements, respectively. The relation with the quantum group approach is discussed.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:modular category, quantum invariant, Vassiliev–Kontsevich invariant, weight system
Language:English
Date:2003
Deposited On:14 Apr 2010 06:35
Last Modified:06 Dec 2017 20:49
Publisher:Mathematical Sciences Publishers
ISSN:1472-2739
Additional Information:© Copyright 2003 Mathematical Sciences Publishers
Publisher DOI:https://doi.org/10.2140/agt.2003.3.969

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