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Quantum relatives of the Alexander polynomial


Author: O. Viro
Translated by: the author
Original publication: Algebra i Analiz, tom 18 (2006), nomer 3.
Journal: St. Petersburg Math. J. 18 (2007), 391-457
MSC (2000): Primary 05C99, 81R99, 57M25
DOI: https://doi.org/10.1090/S1061-0022-07-00956-9
Published electronically: April 11, 2007
MathSciNet review: 2255851
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Abstract | References | Similar Articles | Additional Information

Abstract: The multivariable Conway function is generalized to oriented framed trivalent graphs equipped with additional structure (coloring). This is done via refinements of Reshetikhin-Turaev functors based on irreducible representations of quantized $ \operatorname{gl}(1\vert 1)$ and $ \operatorname{sl}(2)$. The corresponding face state sum models for the generalized Conway function are presented.


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Additional Information

O. Viro
Affiliation: Department of Mathematics, Uppsala University, Box 480, S-751 06 Uppsala, Sweden, and St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email: oleg@math.uu.se

DOI: https://doi.org/10.1090/S1061-0022-07-00956-9
Keywords: Multivariate Conway function, Reshetikhin--Turaev functor, Alexander polynomial, quantum topology, generic graph
Received by editor(s): January 10, 2006
Published electronically: April 11, 2007
Article copyright: © Copyright 2007 American Mathematical Society

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