Classification of string links up to self delta-moves and concordance

Yasuhara, Akira¹

¹Tokyo Gakugei University, Department of Mathematics, Koganeishi, Tokyo 184–8501, Japan

Algebraic and Geometric Topology, Tome 9 (2009) no. 1, pp. 265-275

Résumé

For an n–component string link, the Milnor’s concordance invariant is defined for each sequence I = i1i2⋯im(ij ∈{1,…,n}). Let r(I) denote the maximum number of times that any index appears. We show that two string links are equivalent up to self Δ–moves and concordance if and only if their Milnor invariants coincide for all sequences I with r(I) ≤ 2.

Détail

DOI : 10.2140/agt.2009.9.265

Keywords: string link, $\Delta$–move, self $\Delta$–move, link-homotopy, concordance, self $\Delta$–equivalence, Milnor invariant

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