Can Two-Moves Separate Components of a Link in Knot Theory?

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The discussion focuses on demonstrating that every link is two-equivalent to a trivial link with the same number of components. The initial inquiry involves separating a simple link with a linking number of 1 into its two components and generalizing this for links with n linking numbers. A participant humorously admits to lacking knowledge in knot theory but expresses hope for assistance. Another contributor suggests that two-moves can be shown to encompass a different type of move that effectively separates link components. The conversation highlights the complexity of knot theory and the search for a generalizable solution.
de1irious
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Hi, so I need to show that every link is two-equivalent to a trivial link with the same number of components. Right now I can show that if I have a simple link with linking number = 1, then it is possible to immediately separate the link into its two components. But how can I generalize this idea t links of n linking numbers? Any ideas?

For those interested, this is 3.7 in Invariants of Knots, the Knot Book by Adams.
 
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If it's not theory we can't help you. :-p

I'm sorry, I just couldn't resist the pun. I really should've because I don't know anything about knot theory and I can't actually help you. I hope someone does soon.
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Haha :rolleyes:

Actually I think I figured it out. You can show two-moves contain a certain other kind of move, which more clearly is able to separate components of a link.
 
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