Adelaide Research & Scholarship
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https://hdl.handle.net/2440/92869
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| Type: | Journal article |
| Title: | Markov theorem for free links |
| Author: | Manturov, V. Wang, H. |
| Citation: | Journal of Knot Theory and Its Ramifications, 2012; 21(13):1-23 |
| Publisher: | World Scientific Publishing |
| Issue Date: | 2012 |
| ISSN: | 0218-2165 1793-6527 |
| Statement of Responsibility: | Vassily Olegovich Manturov, Hang Wang |
| 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: | Knots; link; virtual knot; virtual link; free link; free braid; detour move; virtualization move; L-move; Alexander theorem; Markov theorem; Yang-Bajcter equation |
| Rights: | © World Scientific Publishing Company |
| DOI: | 10.1142/S021821651240010X |
| Published version: | http://proxy.library.adelaide.edu.au/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=iih&AN=84391788&site=ehost-live&scope=site |
| Appears in Collections: | Aurora harvest 2 Mathematical Sciences publications |
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