This article is cited in 2 papers

On Milnor's Invariants of 4-Component Links

P. M. Akhmet'ev^a, D. Repovš^b, I. Maleshich<sup>b

a</sup> Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation
^b University of Ljubljana

Abstract: 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.

UDC: 517

Received: 29.11.2000

DOI: 10.4213/mzm361

 English version: Mathematical Notes, 2002, 71:4, 455–463

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