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Strong band sum and dichromatic invariants

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Abstract

Strong band sum is a natural construction from links to dichromatic links. We compute Hoste and Kidwell's dichromatic link invariant of a strong band sum in terms of monochromatic invariants of the data (original link, band). It turns out that the two-variable Conway polynomial of a strong fusion only depends on the monochromatic Conway polynomial of the original link. In particular, it does not depend on the band. Cochran's series of concordance invariants is discussed in this framework.

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References

  • [C1] T. Cochran,Concordance invariance of coefficients of Conway's link polynomial, Invent. Math.82

  • [C2] T. Cochran,Derivatives of links: Milnor's concordance invariants and Massey products, Memoirs of the AMS, No. 427,84 (1990)

  • [F] T. Fiedler,Remark to a paper of Hoste and Przytycki on dichromatic links, Preprint (1991)

  • [HK] J. Hoste and M. E. Kidwell,Dichromatic link invariants, Trans. AMS, No. 1,321 (1990), 197–229

    Article  MATH  MathSciNet  Google Scholar 

  • [HP] J. Hoste and J. H. Przytycki,An invariant of dichromatic links, Proceedings of the AMS (105)4 (1989), 1003–1007

    Article  MathSciNet  Google Scholar 

  • [J] T. Jin,On Kojima's η-function of links, LNiM1350 (1988), 14–30

    Google Scholar 

  • [K1] U. Kaiser,Bands, tangles and linear skein theory, manuscripta math. 71 (1991), 317–336

    MATH  MathSciNet  Google Scholar 

  • [K2] U. Kaiser,Homology Boundary links and fusion constructions II, preprint

  • [Ki] M. E. Kidwell,On the two-variable Conway Potential function, Proc. Amer. Math. Soc.98 (1986), 485–94

    Article  MATH  MathSciNet  Google Scholar 

  • [LM] W. B. R. Lickorish and K. C. Millett,A polynomial invariant of oriented links, Topology No 126 (1987), 107–141

    Article  MATH  MathSciNet  Google Scholar 

  • [R] D Rolfsen,Knots and links, Publish and Perish (1976)

  • [T] L. Traldi,Milnor's invariants and the completion of link modules, Trans. AMS284 (1984), 401–424

    Article  MATH  MathSciNet  Google Scholar 

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  1. Höderlinstr. 3, 5900, Siegen, Germany

    Uwe Kaiser

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  1. Uwe Kaiser
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partially supported by NATO via DAAD

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Kaiser, U. Strong band sum and dichromatic invariants. Manuscripta Math 74, 237–251 (1992). https://doi.org/10.1007/BF02567670

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  • DOI: https://doi.org/10.1007/BF02567670

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