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.
| Original language | English |
|---|---|
| Article number | 1240010 |
| Journal | Journal of Knot Theory and its Ramifications |
| Volume | 21 |
| Issue number | 13 |
| DOIs | |
| State | Published - Nov 2012 |
| Externally published | Yes |
Keywords
- Alexander theorem
- Knots
- L-move
- Markov theorem
- Yang-Baxter equation
- detour move
- free braid
- free link
- link
- virtual knot
- virtual link
- virtualization move