Markov theorem for free links

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. © 2012 World Scientific Publishing Company.

Authors
Manturov V.O. 1 , Wang H.2
Journal
Journal of Knot Theory and its Ramifications
Number of issue
13
Language
English
Status
Published
Link
External link
DOI
10.1142/S021821651240010X
Number
1240010
Volume
21
Year
2012
Organizations
  • 1 Peoples' Friendship University of Russia, Ordjonikidze St., 3, Moscow 119991, Russian Federation
  • 2 Mathematical Sciences Center, Tsinghua University, Jin Chun Yuan West Bldg., Haidian Dist., Beijing 100084, China
Keywords
Alexander theorem; detour move; free braid; free link; Knots; L-move; link; Markov theorem; virtual knot; virtual link; virtualization move; Yang-Baxter equation
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/2244/
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