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Milnor invariants and the
HOMFLYPT Polynomial
Jean-Baptiste Meilhan and Akira Yasuhara |
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Geometry & Topology 16 (2012) 889–917
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Abstract |
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We give formulas expressing Milnor invariants of an –component link in the –sphere in terms of the HOMFLYPT polynomial as follows. If the Milnor invariant vanishes for any sequence with length at most , then any Milnor –invariant with length between and can be represented as a combination of HOMFLYPT polynomial of knots obtained from the link by certain band sum operations. In particular, the “first nonvanishing” Milnor invariants can be always represented as such a linear combination. |
Keywords
Milnor invariant, HOMFLYPT polynomial, clasper, string
link, link-homotopy
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Mathematical Subject Classification 2010
Primary: 57M25, 57M27
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References |
Publication
Received: 28 June 2011
Accepted: 2 February 2012
Published: 19 May 2012
Proposed: Peter Teichner
Seconded: Colin Rourke, Joan Birman
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Authors |
| Jean-Baptiste Meilhan | |
| Institut Fourier Université Grenoble 1 100 rue des Maths BP 74 38402 Saint-Martin d’Hères France |
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| http://www-fourier.ujf-grenoble.fr/~meilhan/ | |
| Akira Yasuhara | |
| Department of Mathematics Tokyo Gakugei University 4-1-1 Nukuikita-Machi Koganei-shi Tokyo 184-8501 Japan |
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| http://www.u-gakugei.ac.jp/~yasuhara/ | |
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