VIRTUAL BRAIDS AND THE L-MOVE
By Louis H. Kauffman, Sofia Lambropoulou. 2005
75 citations recorded by the source corpus.
In this paper we prove a Markov theorem for virtual braids and for analogs of this structure including flat virtual braids and welded braids. The virtual braid group is the natural companion to the category of virtual knots, just as the Artin braid group is the natural companion to classical knots and links. In this paper we follow L-move methods to prove the Virtual Markov theorems. One benefit of this approach is a fully local algebraic formulation of the theorems in each category.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/df6a7b0d09e7575d47259898561a4f2df4b3a772
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In Computational Theory and Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A journey through loop braid groups (2016, background): “In [32] the authors show interest also in certain remarkable quotients of loop braid groups, the symmetric loop braid groups (also known as unrestricted virtual braid groups [37]).”
- K(π, 1) and word problems for infinite type Artin–Tits groups, and applications to virtual braid groups (2012, background): “Like for the classical links and braids, every virtual link is the closure of a virtual braid, and the closures of two virtual braids are equivalent if and only if the braids are related by a finite sequence of moves called virtual Markov moves (see [30,32]).”
- Virtual knots and links (2005, unknown): “For more details see [Kam, Ver, FRR, Ma14, Ma12, KL2 ].”