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Characterization of finite type string link invariants of degree <5

Published online by Cambridge University Press:  16 March 2010

JEAN-BAPTISTE MEILHAN  and
AKIRA YASUHARA
JEAN-BAPTISTE MEILHAN
Affiliation:
Institut Fourier, Université Grenoble 1, 100 rue des Maths - BP 74, 38402 St Martin d'Hères, France. e-mail: jean-baptiste.meilhan@ujf-grenoble.fr
AKIRA YASUHARA
Affiliation:
Tokyo Gakugei University, Department of Mathematics, Koganeishi, Tokyo 184-8501, Japan. e-mail: yasuhara@u-gakugei.ac.jp
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Abstract

We give a complete set of finite type string link invariants of degree <5. In addition to Milnor invariants, these include several string link invariants constructed by evaluating knot invariants on certain closures of (cabled) string links. We show that finite type invariants classify string links up to Ck-moves for k ≤ 5, which proves, at low degree, a conjecture due to Goussarov and Habiro. We also give a similar classification of string links up to Ck-moves and concordance for k ≤ 6.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 148 , Issue 3 , May 2010 , pp. 439 - 472
Copyright
Copyright © Cambridge Philosophical Society 2010

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