Markov theorem for free links

Vassily Olegovich Manturov; Hang Wang

doi:10.1142/S021821651240010X

Markov theorem for free links

Vassily Olegovich Manturov^*
, Hang Wang

^*此作品的通讯作者

科研成果: 期刊稿件 › 文章 › 同行评审

10 引用（Scopus）

摘要

The notion of free link is a generalized notion of virtual link. In this paper we define the group of free braids, prove the Alexander theorem, that all free links can be obtained as closures of free braids and prove a Markov theorem, which gives necessary and sufficient conditions for two free braids to have the same free link closure. Our result is expected to be useful for study of the topology invariants for free knots and links.

源语言	英语
文章编号	1240010
期刊	Journal of Knot Theory and its Ramifications
卷	21
期	13
DOI	https://doi.org/10.1142/S021821651240010X
出版状态	已出版 - 11月 2012
已对外发布	是

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title = "Markov theorem for free links",

abstract = "The notion of free link is a generalized notion of virtual link. In this paper we define the group of free braids, prove the Alexander theorem, that all free links can be obtained as closures of free braids and prove a Markov theorem, which gives necessary and sufficient conditions for two free braids to have the same free link closure. Our result is expected to be useful for study of the topology invariants for free knots and links.",

keywords = "Alexander theorem, Knots, L-move, Markov theorem, Yang-Baxter equation, detour move, free braid, free link, link, virtual knot, virtual link, virtualization move",

author = "Manturov, \{Vassily Olegovich\} and Hang Wang",

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AU - Manturov, Vassily Olegovich

AU - Wang, Hang

PY - 2012/11

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N2 - The notion of free link is a generalized notion of virtual link. In this paper we define the group of free braids, prove the Alexander theorem, that all free links can be obtained as closures of free braids and prove a Markov theorem, which gives necessary and sufficient conditions for two free braids to have the same free link closure. Our result is expected to be useful for study of the topology invariants for free knots and links.

AB - The notion of free link is a generalized notion of virtual link. In this paper we define the group of free braids, prove the Alexander theorem, that all free links can be obtained as closures of free braids and prove a Markov theorem, which gives necessary and sufficient conditions for two free braids to have the same free link closure. Our result is expected to be useful for study of the topology invariants for free knots and links.

KW - Alexander theorem

KW - Knots

KW - L-move

KW - Markov theorem

KW - Yang-Baxter equation

KW - detour move

KW - free braid

KW - free link

KW - link

KW - virtual knot

KW - virtual link

KW - virtualization move

UR - https://www.scopus.com/pages/publications/84868131338

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DO - 10.1142/S021821651240010X

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SN - 0218-2165

VL - 21

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 13

M1 - 1240010

ER -

Markov theorem for free links

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