Virtual Braids and the L–Move
نویسندگان
چکیده
In this paper we prove a Markov Theorem for the virtual braid group and for some analogs of this structure. The virtual braid group is the natural companion to the category of virtual knots, just as the Artin braid group is to classical knots and links. In classical knot theory the braid group gives a fundamental algebraic structure associated with knots. The Alexander Theorem tells us that every knot or link can be isotoped to braid form. The capstone of this relationship is the Markov Theorem, giving necessary and sufficient conditions for two braids to close to the same link (where sameness of two links means that they are ambient isotopic).
منابع مشابه
5 Virtual Braids and the L – Move
In this paper we prove a Markov Theorem for the virtual braid group and for some analogs of this structure. 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 classical knot theory the braid group gives a fundamental algebraic structure associated with knots. The Alexander The...
متن کامل2 00 4 Virtual Braids
Just as classical knots and links can be represented by the closures of braids, so can virtual knots and links be represented by the closures of virtual braids [17]. Virtual braids have a group structure that can be described by generators and relations, generalizing the generators and relations of the classical braid group. This structure of virtual braids is worth study for its own sake. The ...
متن کاملVirtual Braids
Just as classical knots and links can be represented by the closures of braids, so can virtual knots and links be represented by the closures of virtual braids [16]. Virtual braids have a group structure that can be described by generators and relations, generalizing the generators and relations of the classical braid group. This structure of virtual braids is worth study for its own sake. The ...
متن کاملDynnikov coordinates on virtual braid groups
We define Dynnikov coordinates on virtual braid groups. We prove that they are faithful invariants of virtual 2-braids, and present evidence that they are also very powerful invariants for general virtual braids.
متن کامل