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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Virtual Yang-Baxter cocycle invariants


Authors: Jose Ceniceros and Sam Nelson
Journal: Trans. Amer. Math. Soc. 361 (2009), 5263-5283
MSC (2000): Primary 57M27, 18G60
Published electronically: April 8, 2009
MathSciNet review: 2515811
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Abstract: We extend the Yang-Baxter cocycle invariants for virtual knots by augmenting Yang-Baxter 2-cocycles with cocycles from a cohomology theory associated to a virtual biquandle structure. These invariants coincide with the classical Yang-Baxter cocycle invariants for classical knots but provide extra information about virtual knots and links. In particular, they provide a method for detecting non-classicality of virtual knots and links.


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Additional Information

Jose Ceniceros
Affiliation: Department of Mathematics, Whittier College, 13406 Philadelphia, P.O. Box 634, Whittier, California 90608-0634
Email: jcenicer@poets.whittier.edu

Sam Nelson
Affiliation: Department of Mathematics, Claremont McKenna College, 850 Columbia Avenue, Claremont, California 91711
Email: knots@esotericka.org

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04751-5
PII: S 0002-9947(09)04751-5
Received by editor(s): September 6, 2007
Published electronically: April 8, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.