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TitlePolynomial knot and link invariants from the virtual biquandle.
Author(s) Alissa S. Crans, Allison Henrich, Sam Nelson
TypeArticle in Journal
AbstractThe Alexander biquandle of a virtual knot or link is a module over a 2-variable Laurent polynomial ring which is an invariant of virtual knots and links. The elementary ideals of this module are then invariants of virtual isotopy which determine both the generalized Alexander polynomial (also known as the Sawollek polynomial) for virtual knots and the classical Alexander polynomial for classical knots. For a fixed monomial ordering <, the Gröbner bases for these ideals are computable, comparable invariants which fully determine the elementary ideals and which generalize and unify the classical and generalized Alexander polynomials. We provide examples to illustrate the usefulness of these invariants and propose questions for future work.

KeywordsVirtual knot; generalized Alexander polynomial; virtual Alexander polynomial; Sawollek polynomial; biquandle; Alexander biquandle
ISSN0218-2165; 1793-6527/e
URL http://www.worldscientific.com/doi/abs/10.1142/S021821651340004X
JournalJ. Knot Theory Ramifications
PublisherWorld Scientific, Singapore
Translation No
Refereed No