منابع مشابه
On bilinear biquandles
We define a type of biquandle which is a generalization of symplectic quandles. We use the extra structure of these bilinear biquandles to define new knot and link invariants and give some examples.
متن کاملOn Axioms of Biquandles
We prove that the two conditions from the definition of a biquandle by Fenn, Jordan-Santana, Kauffman [1] are equivalent and thus answer a question posed in the paper. We also construct a weak biquandle, which is not a biquandle. According to Fenn, Jordan-Santana and Kauffman [1], biquandles provide powerful invariants of virtual knots and links. It is thus desirable to simplify their axioms as...
متن کاملVirtual Biquandles
In the present paper, we describe new approaches for constructing virtual knot invariants. The main background of this paper comes from formulating and bringing together the ideas of biquandle [KR], [FJK], the virtual quandle [Ma2], the ideas of quaternion biquandles by Roger Fenn and Andrew Bartholomew [BF], the concepts and properties of long virtual knots [Ma11], and other ideas in the inter...
متن کاملSymbolic computation with finite biquandles
A method of computing a basis for the second Yang-Baxter cohomology of a finite biquandle with coefficients in Q and Zp from a matrix presentation of the finite biquandle is described. We also describe a method for computing the Yang-Baxter cocycle invariants of an oriented knot or link represented as a signed Gauss code. We provide a URL for our Maple implementations of these algorithms.
متن کاملClassification of finite Alexander biquandles
We show that two finite Alexander biquandles M and M ′ are isomorphic iff there is an isomorphism of Z[s, t]-modules h : (1 − st)M → (1 − st)M ′ and a bijection g : Os(A) → Os(A ) between the s-orbits of sets of coset representatives of M/(1− st)M and M /(1− st)M ′ respectively satisfying certain compatibility conditions.
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2008
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm112-2-5