Virtual Yang-Baxter cocycle invariants

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.

[1]  Jacquelyn L. Rische,et al.  On bilinear biquandles , 2007, 0708.1951.

[2]  L. Kauffman,et al.  BIQUANDLES FOR VIRTUAL KNOTS , 2007, math/0703216.

[3]  Alissa S. Crans,et al.  Cohomology of Categorical Self-Distributivity , 2006, math/0607417.

[4]  J. Vo,et al.  Matrices and finite biquandles , 2006, math/0601145.

[5]  Sam Nelson,et al.  Symbolic computation with finite biquandles , 2005, J. Symb. Comput..

[6]  M. Saito,et al.  SET-THEORETIC YANG–BAXTER SOLUTIONS VIA FOX CALCULUS , 2005, math/0503166.

[7]  L. Kauffman,et al.  Biquandles and virtual links , 2004 .

[8]  L. Kauffman,et al.  Virtual Biquandles , 2004, math/0411243.

[9]  Nicholas Jackson.  EXTENSIONS OF RACKS AND QUANDLES , 2004, math/0408040.

[10]  M. Elhamdadi,et al.  Homology theory for the set-theoretic Yang–Baxter equation and knot invariants from generalizations of quandles , 2002, math/0206255.

[11]  Nicolas Andruskiewitsch,et al.  From racks to pointed Hopf algebras , 2002, math/0202084.

[12]  L. Kauffman,et al.  Bi-oriented Quantum Algebras, and a Generalized Alexander Polynomial for Virtual Links , 2001, math/0112280.

[13]  M. Elhamdadi,et al.  Twisted quandle homology theory and cocycle knot invariants , 2001, math/0108051.

[14]  S. Kamada,et al.  ABSTRACT LINK DIAGRAMS AND VIRTUAL KNOTS , 2000 .

[15]  Masahico Saito,et al.  Quandle cohomology and state-sum invariants of knotted curves and surfaces , 1999, math/9903135.

[16]  L. Kauffman.  Virtual Knot Theory , 1998, Eur. J. Comb..