Geodesic
On Milnor's Invariants of 4-Component Links
Matematičeskie zametki, Tome 71 (2002) no. 4, pp. 496-507

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We study the behavior of Milnor's $\mu$-invariants of three- and four-component links with respect to the discriminant determined by $\Delta$-moves of links. We introduce a new type of $\Delta$-move, balanced $\Delta$-moves, or, briefly, $B\Delta$-moves. Since each four-component link is equivalent to a standard link under a sequence of balanced $\Delta$-moves, $\Delta$-moves that involve at most two components, and Reidemeister moves, we manage to define axiomatically $\mu$-invariants of length 3 for arbitrary semibounding links. 
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     title = {On {Milnor's} {Invariants} of {4-Component} {Links}},
     journal = {Matemati\v{c}eskie zametki},
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P. M. Akhmet'ev; D. Repovš; I. Maleshich. On Milnor's Invariants of 4-Component Links. Matematičeskie zametki, Tome 71 (2002) no. 4, pp. 496-507. http://geodesic.mathdoc.fr/item/MZM_2002_71_4_a1/