Volume 9, issue 1 (2009)

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

Akira Yasuhara

Algebraic & Geometric Topology 9 (2009) 265–275
Abstract

For an n–component string link, the Milnor’s concordance invariant is defined for each sequence I = i1i2im(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.

Keywords
string link, $\Delta$–move, self $\Delta$–move, link-homotopy, concordance, self $\Delta$–equivalence, Milnor invariant
Mathematical Subject Classification 2000
Primary: 57M25, 57M27
References
Publication
Received: 6 July 2008
Revised: 26 November 2008
Accepted: 19 December 2008
Published: 13 February 2009
Authors
Akira Yasuhara
Tokyo Gakugei University
Department of Mathematics
Koganeishi
Tokyo 184–8501
Japan