Biquandles and virtual links

By R. Fenn, Mercedes Jordan-Santana, Louis H. Kauffman. 2004

154 citations recorded by the source corpus.

Abstract In this paper we define a birack and a biquandle, generalizing the notion of a rack and a quandle. This gives rise to natural invariants of virtual knots and braids. Some of the properties of biracks and biquandles are explained in this paper. Applications to particular virtual braids and links are given.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ca29ae5879eafa60efa91d2c381c5dac371325d7

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Virtual knots and links (2005, methodology): “As survey papers on virtual knot theory, we recommend [23, 33, 32, 25, 22, 7, 6 ].”
Homology theory for the set-theoretic Yang–Baxter equation and knot invariants from generalizations of quandles (2002, methodology): “The definition of the type I condition in [1, 13] is differently formulated but they prove that their definition is equivalent to the above condition.”
Virtual knot theory-unsolved problems (2005, unknown): “See [2] [3] [4] [5] [9] [10] [11] [12] [8] [13] [16] [17] [18] [19] [20] [22] [23] [24] [25] [26] [31] [33] [34] [36] [37] [38] [39] [40] [41] [43] [50] [51] [55] [58] [59] [60] [61] [62] [64] [65] [67] [68] [70] [72] [73] [74] [75] [76] [78] [79] [80] [81] [82] [84] [86] [87] [88] [83] [90] [93]…”
Matrices and finite biquandles (2006, background): “K eyw ords:Finite biquandles,virtualknots,knotinvariants 2000 M SC :57M 25,57M 27”