Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

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
Published electronically: April 11, 2007
MathSciNet review: 2255851
Full-text PDF Free Access

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2000): 05C99, 81R99, 57M25

Retrieve articles in all journals with MSC (2000): 05C99, 81R99, 57M25


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: http://dx.doi.org/10.1090/S1061-0022-07-00956-9
PII: S 1061-0022(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